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Term Structure Forecasting Using Macro Factors And Forecast Combination1

Michiel De Pooter, Francesco Ravazzolo, and Dick van Dijk2

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at http://www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at http://www.ssrn.com/.


Abstract:

We examine the importance of incorporating macroeconomic information and, in particular, accounting for model uncertainty when forecasting the term structure of U.S. interest rates. We start off by analyzing and comparing the forecast performance of several individual term structure models. Our results confirm and extend results found in previous literature that adding macroeconomic information, through factors extracted from a large number of individual series, tends to improve interest rate forecasts. We then show, however, that the predictive power of individual models varies over time significantly. Models with macro factors are the more accurate in and around recession periods. Models without macro factors do particularly well in low-volatility subperiods such as the late 1990s. We demonstrate that this problem of model uncertainty can be mitigated by combining individual model forecasts. Combining forecasts leads to encouraging gains in predictability, especially for longer-dated maturities, and importantly, these gains are consistent over time.

Keywords: Term structure of interest rates, Nelson-Siegel model, affine term structure model, macro factors, forecast combination, model confidence set

JEL classification: C5, C11, C32, E43, E47


1  Introduction

Modelling and forecasting the term structure of interest rates is by no means an easy endeavor. Since long yields are risk-adjusted averages of expected future short rates, yields of different maturities are intimately related and therefore move together, in the cross-section as well as over time. At the same time, long and short maturities tend to react quite differently to shocks hitting the economy. Furthermore, monetary policy authorities such as the Federal Reserve are actively targeting the short end of the yield curve to achieve their macroeconomic goals. In general, many forces are at work at moving interest rates. Identifying these forces and understanding their impact on yields, is therefore of crucial importance.

In recent years, significant progress has been made in modelling the term structure of interest rates, which has come about mainly through the development of no-arbitrage factor models. The literature on these so-called affine term structure models was kick-started by seminal papers of Vasicek (1977) and Cox, Ingersol, and lRoss (1985), characterized by Duffie and Kan (1996) and classified by Dai and Singleton (2000). A survey of issues involving the specification and estimation of affine models set in continuous time is Piazzesi (2003). Discrete-time models are discussed in detail in Backus, Foresi, and Telmer (1998). Traditional affine models explain yield movements as being driven by a small number of (latent) factors that can be extracted from the panel of yields across time and across maturities, and impose cross-equation restrictions which are consistent with no-arbitrage. Affine models, provided they are properly specified, have been shown to accurately fit the term structure, see for example Dai and Singleton (2000). These models are rather silent, however, about the links between the (mainly) statistical yield factors and macroeconomic forces.

The current term structure literature is actively progressing to resolve this missing link. Recent studies have yielded interesting approaches for studying the joint behavior of interest rates and macroeconomic variables. One avenue that has been taken is to extend existing term structure models by adding in observed macroeconomic variables, and to study their interactions with the latent factors. A seminal contribution to this strand of the literature is Ang and Piazzesi (2003), who were the first to augment a standard three-factor affine model with macroeconomic variables. Studies such as Kim and Wright (2005), Dai and Philippon (2006), DeWachter and Lyrio (2006), Ang, Dong, and Piazzesi (2007), and Bikbov and Chernov (2008), among others, also incorporate various macroeconomic variables and study their explanatory power for yield movements. Studies that take a more structural approach include those by Wu (2005), Hordahl, Tristani, and Vestin (2006), and Rudebusch and Wu (2008), who all combine a model for the macro economy with an arbitrage-free specification for the term structure. Moving away from the realm of no-arbitrage interest rate models to that of more ad-hoc models, in particular the popular Nelson and Siegel (1987) model, studies such as Diebold, Rudebusch, and Aruoba (2006) and Monch (2006) also show that adding information which reflects the state of the economy is beneficial for explaining the level of interest rates.3

Whereas fitting interest rate movements over time is already a strenuous task, accurately forecasting future interest rate levels is an even more difficult challenge. Yields of all maturities are close to being non-stationary, which makes it hard for any model to outperform the simple random walk no-change forecast. Several studies have documented that beating the random walk in terms of forecasting accuracy is indeed difficult, in particular for unrestricted yields-only vector autoregressive (VAR) and standard affine models, see Duffee (2002) and Ang and Piazzesi (2003). Recently, however, more favorable evidence for interest rate predictability has been reported. Duffee (2002) shows that more flexible affine specifications can beat the random walk. Diebold and Li (2006) and Christensen, Diebold, and Rudebusch (2009) show that dynamic Nelson-Siegel-style factor models forecast particularly well. Even more promising results are obtained with models that incorporate macroeconomic information. Ang and Piazzesi (2003) and Mönch (2008) report improved forecasts for U.S. Treasury yields at various horizons using affine models which have been augmented to include principal component-based macro factors. Hordahl, Tristani, and Vestin (2006) report similar improvements in predictability for German zero-coupon bond yields using inflation and industrial production. Ludvigson and Ng (2009) find that macro factors also help to forecast excess bond returns, indicating that macro factors contain predictive information that is not already contained in forward rates and yield spreads.

When examining the historical time series of U.S. interest rates we can easily identify subperiods across which yield curve dynamics appear to be quite different. This not only concerns characteristics such as the level and slope of the yield curve, but also the "stability" of the curve, that is, interest rate volatility. For example, the second half of the 1990s during which the yield curve was fairly stable, was followed by a strong and fast decline in interest rate levels in the early 2000s, accompanied by a pronounced widening of spreads when the Fed eased monetary policy in light of the burst of the dot-com bubble and the subsequent recession. Formal evidence of these kinds of different interest rate regimes is presented for example in Ang and Bekaert (2002).4 It seems an overly daunting requirement for any individual model to be capable of consistently producing accurate forecasts under potentially very different interest rate regimes. In this paper, it is exactly this premise that we investigate for the term structure of U.S. interest rates. In order to do so we analyze a range of different models, from simple univariate autoregressive models to multivariate specifications with no-arbitrage restrictions, and we assess their forecasting performance over time.

We analyze each model in our model set with and without adding macroeconomic information to it. More specifically, we add macro factors, which we extract from a large set of individual macroeconomic variables. As noted above, several recent studies have shown that adding macroeconomic variables to term structure models helps to explain and forecast yield movements. Additionally, papers such as Ang and Piazzesi (2003), Monch (2008) and Ludvigson and Ng (2009) document that using macro factors, extracted from a large panel of macro series, instead of individual series works well in affine models. We examine and extend this evidence by incorporating these types of macro diffusion indices also in the Nelson-Siegel model, as well as in simpler AR and VAR models. Our results show that adding macro factors does indeed improve the forecast accuracy of individual models. This only seems to be the case in particular interest rate regimes, however, and results vary across the term structure. As we demonstrate below, and which is part of the main message of this paper, we find that the predictive performance of individual models indeed varies over time considerably. Models that incorporate macroeconomic information are more accurate in subperiods with substantial uncertainty about the future path of interest rates. An example of a regime like this is in and around the 2001 recession. Models that do not include macroeconomic information do particularly well in subperiods where the term structure has a more stable pattern, or when the spread between long and short yields closes, as was the case in the second half of the 1990s for example.

The fact that different models forecast well in different subperiods confirms ex-post that different model specifications play a complementary role in approximating the unobserved data generating process of interest rates. Our results provide a strong incentive for examining forecast combination techniques as an alternative to believing in single models. We find that combining forecasts across all individual models, with and without macro factors, and after trimming out the worst performing models via Model Confidence Set tests as in Hansen, Lunde, and Nason (2003) gives accurate forecasts for short forecast horizons. Forecast combinations of just those models that include macro information, using a weighting method that is based on relative historical performance over a long sample, results in improved forecasts for long forecast horizons. Forecast accuracy in the latter case is particularly encouraging for longer-dated maturities, which traditionally have been difficult to forecast.

The remainder of the paper is organized as follows. In Section 2 we discuss the panel of U.S. Treasury yields we analyze in this study, and we provide details on the panel of macro series that we use in constructing our macro factors. We devote Section 3 to present the set of individual models in our model consideration set. In Section 4 we discuss forecast results of these individual models whereas in Section 5 we outline and analyze results of several forecast combination schemes. Finally, in Section 6 we conclude. The Appendices provide technical details on model inference and forecast evaluation criteria.

2  Data

2.1  Yield Data

Our term structure dataset consists of constant maturity, end-of-month continuously compounded yields on U.S. zero-coupon bonds. These have been constructed from average bid-ask price quotes on U.S. Treasuries from the CRSP government bond files. CRSP filters the available quotes by taking out illiquid bonds and bonds with option features. The remaining quotes are used to construct forward rates using the Fama and Bliss (1987) bootstrap method, as outlined in Bliss (1997). The forward rates are then averaged to construct constant maturity spot rates.5 Similar to Diebold and Li (2006) and Monch (2008), our dataset consists of unsmoothed Fama-Bliss yields. These unsmoothed yields exactly price the underlying U.S. Treasury securities.

Throughout our analysis we use yields for $ N=13$ different maturities; $ \tau=$ 1, 3 and 6 months and 1, 2,$ \ldots$, 10 years. We denote time-$ t$ yields by $ y_{t}^{(\tau_{i})}$ for $ i=1,\ldots,N$. For the Nelson-Siegel models we follow Diebold and Li (2006) and Diebold, Rudebusch, and Aruoba (2006) by including additional maturities of 9, 15, 18, 21 and 30 months in order to increase the number of yield observations at the short end of the curve. Our sample period covers January 1970 till December 2003 for a total of 408 monthly observations. Similar to Duffee (2002) and Ang and Piazzesi (2003) we include data from well before the Volcker disinflation period, despite the reservations expressed in Rudebusch and Wu (2008) that it is likely that the pricing of interest rate risk and the relationship between yields and macroeconomic variables have changed during such a long time span. We do so for two reasons: (i) to have enough observations to identify the parameters of the models in our model consideration set with sufficient accuracy, as some models are highly parameterized, and (ii) to be able to assess forecasting performance over sufficiently long (sub-)periods with different yield curve characteristics.

The downside of using the Bliss dataset is that it stops at the end of 2003, well before the financial turmoil that started around July 2008 and which is obviously an interesting period during which to gauge the time-varying forecasting performance of various yield curve models. Two widely-used alternative datasets that contain more recent data are the Fama-Bliss CRSP dataset which is currently updated until the end of 2008, and the real-time dataset of Gurkaynak, Sack, and Wright (2007) (GSW) which is available from the Federal Reserve Board's website. The CRSP dataset only contains maturities up until five years, however, whereas one of our aims in this paper is to study model forecasting performance for longer-dated yields. The drawback of the GSW dataset is that it consists of smoothed fitted yields using the Svensson (1994) extension of the Nelson and Siegel (1987) model. Since we include the two-step Nelson-Siegel specification of Diebold and Li (2006) as one of the models in our model consideration set (albeit that our first-round fitting step uses the original Nelson-Siegel model and not the Svensson extension as in GSW) we do not want to give this approach a potentially unfair advantage.

Figure 1(a) shows time-series plots for a subsample of the 13 maturities in our dataset whereas Table 1 reports summary statistics. The stylized facts common to yield curve data are clearly present: the sample average curve is upward sloping and concave, volatility is decreasing with maturity, autocorrelations are very high and increasing with maturity, and normality is rejected due to positive skewness and excess kurtosis. Correlations between yields of different maturities are high, especially for similar maturities. Even the maturities which are furthest apart (1 month and 10 years) still have a full-sample correlation as high as 86%.

2.2  Macroeconomic Data

Our macroeconomic dataset originates from Stock and Watson (2005) and consists of 116 series. Our macro dataset is the same as that of Ludvigson and Ng (2009). Contrary to Ludvigson and Ng (2009), however, we excluded all interest rate and interest rate spread-related series from the original 132 series in the dataset, discarding 16 series in total. We do include the federal funds rate as being an instrument for the stance of the Fed's monetary policy. The macro variables are classified in 15 categories: (1) output and income, (2) employment and hours, (3) retail, (4) manufacturing and trade sales, (5) consumption, (6) housing starts and sales, (7) inventories, (8) orders, (9) stock prices, (10) exchange rates, (11) federal funds rate, (12) money and credit quantity aggregates, (13) price indices, (14) average hourly earnings and (15) miscellaneous. Table 2 lists the series included in the macro dataset and the category they are classified in.

We transform the monthly recorded macro series, whenever necessary, to ensure stationarity by using log levels, annual differences or annual log differences. Column 2 of Table 2 lists the transformations. Outliers in each individual series are recursively replaced by the median value of the previous five observations, see Stock and Watson (2005) for details. We follow Ang and Piazzesi (2003), Diebold, Rudebusch, and Aruoba (2006), and Monch (2008) and in our use of annual growth rates. Monthly growth rates series are very noisy and are therefore expected to add little information when added to the various term structure models.

We need to be careful about the timing of the macro series relative to the interest rate series to prevent the use of information that has not been released yet at the time when a forecast is made. This in order to make this a realistic pseudo real-time out-of-sample forecasting exercise. The interest rates in our dataset are recorded at the end of the month. Although macro figures tend to be released at the beginning or in the middle of the month, they are typically released with a lag of one up to several several months. We accommodate for a potential look-ahead bias by lagging all macro series by one month, except for financial series; stock index variables, exchange rates and the federal funds rate, which are all monthly averages.6

Similar to Monch (2008) and Ludvigson and Ng (2009), we extract a small number of common factors from our macro dataset. Monch (2008), based on the work of Bernanke, Boivin, and Eliasz (2005), builds a no-arbitrage Factor-Augmented term structure model with four factors from a large panel of macroeconomic variables whereas Ludvigson and Ng (2009) use macro factors to predict excess bond returns. As in these papers, we apply principal component analysis to obtain macro factors from the full panel of macro series. Before extracting principal component factors, we first standardize all the series to have zero mean and unit variance, see Stock and Watson (2002a, b) for details. The use of common factors instead of individual macro series allows us to incorporate a much richer information set beyond that contained in often used variables such as CPI, PPI, employment, output gap or capacity utilization alone, while at the same time ensuring that the number of model parameters remains manageable.

For the full sample period, the first common macro factor explains 35% of the variation in the macro panel. The second and third factors explain an additional 19% and 8%, respectively, whereas the first 10 factors together explain an impressive 85%. Figure 2 shows the $ R^{2}$ when regressing each individual macro series on each of first three factors separately. These types of regressions allows us to attach economic labels to the factors and to interpret them more as representing meaningful economic variables instead of simply as artifacts from a statistical procedure. The first factor closely resembles the series in the real output and employment categories (categories 1 and 2), as well as categories 3 through 8, and can therefore be labelled business cycle or real activity factor. The second factor loads mostly on inflation measures (category 13) which allows for the label of inflation factor. The third factor, although the correlations are much lower than for the first and second factor, is mostly related to money stock and reserves (category 12) and could thus be labelled a monetary aggregates or money stock factor. Figure 3 corroborates these interpretations graphically through time-series plots of the three macro factors together with industrial production (total), consumer price index (all items) and money stock (M1), respectively.

We have chosen to include the first three factors as exogenous explanatory variables in the various term structure models because, together, these factors explain over 60% of the variation in the macro panel.7 Given that we want to construct interest rate forecasts we also need to select a model to forecast the macro factors. We discuss this in more detail in Section 3.1.

3  Models

We assess the individual and combined forecasting performance of a range of models that are commonly used in the literature as well as by practitioners. Since previous studies have shown that parsimonious models often outperform more sophisticated models, we consider models with different levels of complexity. Our model set ranges from unrestricted linear specifications for yield levels (AR and VAR models), models that impose a parametric structure on factor loadings (the Nelson-Siegel class of models), to models that impose cross-sectional restrictions to rule out arbitrage opportunities (affine models). Our benchmark model throughout out forecasting exercise is the random walk model.

We could in principle consider an almost unlimited number of different models. For example, one can think of lots of different models resulting from including various (subsets of) individual macro variables, such as the models of Diebold, Rudebusch, and Aruoba (2006) and Hordahl, Tristani, and Vestin (2006). Although it is true that these models can me more economically meaningful than some of the models we examine, considering each and every one of these would blow up the number of models in our consideration set. To keep the number manageable, we therefore consider only a small but representable subset of models. Furthermore, we circumvent the decision of which individual macro variables to include by basically including all of them through our macro factor approach.

In this section we present the different models. We defer all specific details regarding inference and generating (multi-step ahead) forecasts to Appendix A.

3.1  Incorporating Macro Factors

The approach we use to incorporate the three macro factors is the following. Denote $ M_{t}$ as the $ (3 \times1)$ vector containing the time-$ t$ values of the macro factors. We add the factors to each term structure model, contemporaneously as well as lagged by one month to capture any delayed effects of macroeconomic news on the term structure.8 The exogenous explanatory macro information we add to the models is denoted by $ X_{t}$, and is thus given by $ X_{t}=(M_{t}^{\prime}$ $ M_{t-1}^{\prime})^{\prime}$.

Our approach implies that when we forecast yields, we also need to model and forecast the macro factors. We tackle this issue by following AngPiazzesi2003 in only allowing for a unidirectional link from macro variables to yields. Although this can be argued to be a restrictive assumption as it does not allow for a potentially rich bidirectional feedback, it enables us to model the time-series behavior of the macro factors separate from that of yields, which considerably facilitates estimation.9 Information criteria suggest modeling and forecasting $ M_{t}$ using a VAR model with three lags:

$\displaystyle M_{t}=c+\Phi_{1} M_{t-1}+\Phi_{2} M_{t-2}+\Phi_{3} M_{t-3}+\xi_{t},\qquad\eps_{t}\sim\mathcal{N}\left( 0,H\right)$ (1)

where $ c$ is a $ (3 \times1)$ vector, $ \Phi_{i}$ is a $ (3 \times3)$ matrix for $ i=1,\ldots,3$, and $ H$ is a $ (3 \times3)$ unrestricted covariance matrix. Forecasts of future factor values can be constructed by forward iteration of the estimated relationship in (1).

3.2  Interest Rate Models

Random Walk

The first model that we consider is a random walk without drift for each individual maturity $ \tau_{i}$, $ i=1,\ldots,N$,

$\displaystyle y_{t}^{(\tau_{i})}=y_{t-1}^{(\tau_{i})}+\eps_{t}^{(\tau_{i})}, \qquad\eps_{t}^{(\tau_{i})}\sim\mathcal{N}\left( 0,{\sigma^{(\tau_{i})}} ^{2}\right)$ (2)

In this model any $ h$-step ahead forecast $ \hat{y}_{T+h}^{(\tau_{i})}$ is simply equal to the most recently observed value $ y_{T}^{(\tau_{i})}$. It is natural to consider this no-change model as the benchmark against which to judge the predictive power of other models, and we do so throughout the paper. Table 1 confirms that yields are indeed all but non-stationary as the reported first-order autocorrelation coefficients are all very close to unity. Duffee (2002), Ang and Piazzesi (2003), Diebold and Li (2006), and Monch (2008) all show, using different models and different forecast periods, that beating the random walk in terms of forecasting performance is quite an arduous task. We denote the random walk model by the abbreviation RW.

AR Model

Although (unreported) results indicate that the null of a unit root for yield levels cannot be rejected statistically, the assumption of nonstationary yields is difficult to interpret from an economic point of view. Nonstationarity implies that interest rates can roam around freely and do not revert back to a long-term mean, something which contradicts the Federal Reserve's monetary policy objective of moderate long-term interest rates. The second model that we consider therefore is a first-order univariate autoregressive model which allows for mean-reversion,

$\displaystyle y_{t}^{(\tau_{i})}=c^{(\tau_{i})}+\phi^{(\tau_{i})}y_{t-1} ^{(\tau_{i})}+{\psi^{(\tau_{i})}}^{\prime}X_{t}+\eps_{t}^{(\tau_{i})}, \qquad\eps_{t}^{(\tau_{i})}\sim\mathcal{N}\left( 0,{\sigma^{(\tau_{i})}} ^{2}\right)$ (3)

where $ c^{(\tau_{i})}, \phi^{(\tau_{i})}$ and $ \sigma^{(\tau_{i})}$ are scalar parameters and $ \psi^{(\tau_{i})}$ is a $ (6 \times1)$ vector containing the coefficients on the macro factors. We construct forecasts both with and without macro factors by setting $ \psi^{(\tau_{i})}=0$. We denote the yield-only model by AR and the model with macro factors by AR-X. For this and all other models we construct iterated $ h$-step ahead forecasts. Another approach is to construct direct forecasts, by regressing $ y_{t}^{(\tau_{i})}$ directly on its $ h$-month lagged value $ y_{t-h}^{(\tau_{i})}$ as in Diebold and Li (2006). For the state-space form of the Nelson-Siegel model and the affine model such an approach is, however, uncommon. For the sake of consistency, we therefore chose to use iterated forecasts for all the models. Whether iterated forecasts are more accurate than direct forecasts is still an ongoing debate, see for example the recent discussion in Marcellino, Stock, and Watson (2006). In the context of interest rate forecasting, Carriero, Kapetanios, and Marcellino (2009) find that for linear AR and VAR models the iterated approach produces better forecasts than the direct approach.

VAR Model

Vector autoregressive (VAR) models allow for using the history of other maturities as additional information on top of any maturity's own history. We use the following first-order VAR specification,10

$\displaystyle Y_{t} = c + \Phi Y_{t-1}+\Psi X_{t}+H\eps_{t},\qquad\eps_{t} \sim\mathcal{N}\left( 0,\text{I}\right)$ (4)

where $ Y_{t}$ contains the yields for all 13 maturities; $ Y_{t}=[y_{t} ^{(1m)},\ldots,y_{t}^{(10y)}]^{\prime}$, $ c$ is a $ (13 \times1)$ vector, $ \Phi$ a $ (13 \times13)$ matrix, $ \Psi$ a $ (13 \times6)$ matrix, and $ H$ is the (unrestricted) residual variance matrix containing $ \frac{1}{2}N(N+1)=91$ free parameters. Our approach is similar in spirit to the VAR models used in Evans and Marshall (1998), Evans and Marshall (2007) and Ang and Piazzesi (2003) in the sense that we impose exogeneity of macroeconomic variables with respect to yields.

A well-known drawback of using an unrestricted VAR model for yields is that forecasts can only be constructed for those maturities that are actually included in the model. Since we want to construct forecasts for thirteen maturities, this results in a substantial number of parameters that need to be estimated. In an attempt to mitigate estimation error and, consequently, to reduce the forecast error variance, we instead summarize the information contained in the explanatory vector $ Y_{t-1}$ by replacing it with a small number of common yield curve factors. Similar to Litterman and Scheinkman (1991) and many other studies, we find that the first 3 principal components explain almost all the variation in the cross section of yields (over 99% for the full sample). Accordingly, we replace $ Y_{t-1}$ in (4) with the $ (3 \times1)$ vector of yield factors $ F_{t-1}$:

$\displaystyle Y_{t} = c + \Phi F_{t-1}+\Psi X_{t}+\eps_{t},\qquad\eps_{t} \sim\mathcal{N}\left( 0,\text{H}\right)$ (5)

where $ \Phi$ is now a $ (13 \times3)$ matrix. The VAR model without and with macroeconomic variables is denoted by VAR and VAR-X, respectively.

Nelson-Siegel Model

Diebold and Li (2006) show that using the in essence static Nelson and Siegel (1987) model as a dynamic factor model generates highly accurate interest rate forecasts. The Nelson-Siegel model differs from the unrestricted VAR model in (5) in that it imposes a parametric structure on the factor loadings. The factor loadings $ \Phi$ are specified as exponential functions of time to maturity and a single parameter $ \lambda$. Following Diebold, Rudebusch, and Aruoba (2006), the state-space representation of the three-factor model, with a first-order autoregressive model for the dynamics of the state vector, is given by

$\displaystyle y_{t}^{(\tau_{i})}$ $\displaystyle =\! \beta_{1,t} + \beta_{2,t} \left[ \frac {1\!-\!\exp(-\tau_{i}/\lambda)}{\tau_{i}/\lambda} \right] + \beta_{3,t} \left[ \frac{1\!-\!\exp(-\tau_{i}/\lambda)}{\tau_{i}/\lambda}\! -\! \exp(-\tau_{i}/\lambda) \right] +\eps_{t}^{(\tau_{i})}$ (6)
$\displaystyle \beta_{t}$ $\displaystyle =\!a+\Gamma\beta_{t-1}+u_{t}$ (7)

The state vector, $ \beta_{t}=(\beta_{1,t},\beta_{2,t},\beta_{3,t})^{\prime}$, contains the latent factors at time $ t$ which can be interpreted as level, slope and curvature factors, respectively (see Diebold and Li (2006) for details). The parameter $ \lambda$ governs the exponential decay towards zero of the factor loadings on $ \beta_{2,t}$ and $ \beta_{3,t}$, $ a$ is a $ (3 \times1)$ vector of parameters, and $ \Gamma$ is a $ (3\times3)$ parameter matrix. We assume that the measurement equation and state equation errors in (6) and (7) are normally distributed and mutually uncorrelated;

$\displaystyle \left[ \begin{array}[c]{c} \eps_{t}\\ u_{t} \end{array} \right] \sim\mathcal{N}\bigg(\left[ \begin{array}[c]{c} 0_{18\times1}\\ 0_{3 \times1} \end{array} \right] , \left[ \begin{array}[c]{cc} H & 0\\ 0 & Q \end{array} \right] \bigg)$ (8)

where $ H$ is a diagonal $ (18 \times18)$ matrix and $ Q$ a full $ (3 \times3)$ matrix. We follow Diebold and Li (2006) by adding five maturities ($ \tau=$ 9, 15, 18, 21 and 30 months) to the short end of the yield curve to estimate the Nelson-Siegel model in (6)-(8). To estimate the Nelson-Siegel model, we use two different estimation procedures: a two-step approach and a one-step approach.

The two-step approach is used in Diebold and Li (2006) and consists of first estimating the latent factors in $ \beta_{t}$ using the cross-section of yields for each month $ t$, while fixing $ \lambda$. Given the estimated time-series for the factors, the second step then consists of modeling the dynamics of the factors in (7) by fitting either a joint VAR(1) model, or by estimating separate AR(1) models, thereby assuming that both $ \Gamma$ and $ Q$ are diagonal. We denote these approaches by NS2-VAR and NS2-AR, respectively. The one-step approach follows from Diebold, Rudebusch, and Aruoba (2006) and involves jointly estimating (6)-(8) as a state space model using the Kalman filter. In this approach we assume that $ \Gamma$ and $ Q$ are both full matrices, while $ \lambda$ is now estimated alongside the other parameters. We denote the one-step approach by NS1.

Diebold, Rudebusch, and Aruoba (2006) show how to extend the Nelson-Siegel model to incorporate macroeconomic variables by adding these as observable factors to the state vector, and then writing the model in companion form:

$\displaystyle y_{t}^{(\tau_{i})}$ $\displaystyle =\! \beta_{1,t} + \beta_{2,t} \!\!\left[ \!\frac{1\!-\!\exp(-\tau_{i}/\lambda)}{\tau_{i}/\lambda} \right] + \beta_{3,t} \!\!\left[ \! \frac{1\!-\!\exp(-\tau_{i}/\lambda)}{\tau _{i}/\lambda}\! -\! \exp(-\tau_{i}/\lambda) \right] +\eps_{t}^{(\tau_{i} )}$ (9)
$\displaystyle f_{t}$ $\displaystyle =\!a+\Gamma f_{t-1}+\eta_{t}$ (10)
$\displaystyle \left[ \begin{array}[c]{c} \eps_{t}\\ \eta_{t} \end{array} \right]$ $\displaystyle \sim\mathcal{N}\bigg(\left[ \begin{array}[c]{c} 0_{18\times1}\\ 0_{12 \times1} \end{array} \right] , \left[ \begin{array}[c]{cc} H & 0\\ 0 & Q \end{array} \right] \bigg)$ (11)

The state vector now also contains observable factors; $ f_{t}=(\beta _{1,t},\beta_{2,t},\beta_{3,t},M_{t},M_{t-1},M_{t-2})$ .11 The dimensions of $ a$, $ \Gamma$ and $ Q$ are increased appropriately and $ \eta_{t}$ is now given by $ \eta_{t}=(u_{t}^{\prime},\xi _{t}^{\prime},0,\ldots,0)^{\prime}$ . We impose structure on $ \Gamma$ and $ Q$ to accommodate for the effects of lagged macro factors while maintaining the unidirectional causality from macro factors to yields only.12 In particular, the lower left ($ 9 \times3$) block of $ \Gamma$ consists of zeros whereas $ Q$ is block diagonal with a non-zero $ (3 \times3)$ block $ Q_{\beta}$ for the yield factors and a non-zero $ (3 \times3)$ block $ Q_{M}$ for the contemporaneous macro factors. All other blocks on the diagonal contain zeros only. The Nelson-Siegel model with macro factors can also again be estimated by using either a two-step approach with AR or VAR dynamics for the yield factors, which we denote by NS2-AR-X and NS2-VAR-X, respectively, or by using the one-step approach, which we denote by NS1-X. Another potential specification of the Nelson-Siegel model would be that of Christensen, Diebold, and Rudebusch (2009) who adjust the Nelson-Siegel model to make it consistent with arbitrage-free models (to be discussed in the next section). Although Christensen, Diebold, and Rudebusch (2009) show that the Arbitrage-Free Dynamic Nelson-Siegel (AFDNS) model forecasts well out-of-sample, Carriero, Kapetanios, Marcellino (2009), using a longer forecasting sample, report that the performance of the AFDNS model is not that different from the two-step Nelson-Siegel model. Because our model set is already large as it is, we therefore chose not to include the AFDNS model in our model set.

Affine Model

Models that impose no-arbitrage restrictions have been examined for their forecast accuracy in for example Duffee (2002), Ang and Piazzesi (2003) and Mönch (2008). The attractive property of the class of no-arbitrage models is that sound theoretical cross-sectional restrictions are imposed on factor loadings to rule out arbitrage opportunities. In this paper we consider a Gaussian-type discrete time affine no-arbitrage model, using a set-up similar to Ang and Piazzesi (2003). In particular, we assume that movements in the yield curve are driven by a vector of $ K$ underlying state variables, $ Z_{t}$, which we assume follows a Gaussian VAR(1) process

$\displaystyle Z_{t}=\mu+\Psi Z_{t-1}+u_{t},\qquad u_{t}\sim\mathcal{N} \left( 0,\Sigma\Sigma^{\prime}\right)$ (12)

where $ \Sigma$ is a $ (K \times K)$ lower triangular Choleski matrix, $ \mu$ a $ (K \times1)$ parameter vector and $ \Psi$ a $ (K \times K)$ parameter matrix.

The short interest rate is assumed to be an affine function of the factors

$\displaystyle r_{t}=\delta_{0}+\delta_{1}^{\prime}Z_{t}$ (13)

where $ \delta_{0}$ is a scalar and $ \delta_{1}$ a $ (K \times1)$ vector. We adopt a standard form for the pricing kernel, which is assumed to price all assets in the economy,

$\displaystyle m_{t+1} = \exp\!{\big(\!-\!r_{t}-\frac{1}{2}\lambda_{t}^{\prime}\lambda _{t}-\lambda_{t}^{\prime}u_{t+1}\big)} \non$  

We specify market prices of risk to be time-varying and affine in the state variables

$\displaystyle \lambda_{t}=\lambda_{0}+\lambda_{1}Z_{t}$ (14)

with $ \lambda_{0}$ a $ (K \times1)$ vector and $ \lambda_{1}$ a $ (K \times K)$ matrix. Risk premia are constant over time if $ \lambda_{1}$ is equal to a zero matrix. When $ \lambda_{0}$ is also equal to zero, risk premia are zero altogether.

Under the above assumptions it can be shown that bond prices are an exponentially-affine function of the state variables,

$\displaystyle P_{t}^{(\tau)}=\exp[A^{(\tau)}+{B^{(\tau)} }^{\prime}Z_{t}]$ (15)

We can recursively determine the price of a $ \tau-$period bond using

$\displaystyle P_{t}^{(\tau)}=\mathbb{E}_{t}[m_{t+1} P_{t+1}^{(\tau-1)}]$ (16)

where the expectation is taken under the risk-neutral measure. Ang and Piazzesi (2003), among others, show that this gives the following recursive formulas for the bond pricing coefficients $ A^{(\tau)}$ and $ B^{(\tau)}$:

$\displaystyle A^{(\tau+1)}$ $\displaystyle =A^{(\tau)}+{B^{(\tau)}}^{\prime}[\mu-\Sigma\lambda_{0} ]+\frac{1}{2}{B^{(\tau)}}^{\prime}\Sigma\Sigma^{\prime(\tau)}-\delta _{0}$ (17)
$\displaystyle {B^{(\tau+1)}}^{\prime}$ $\displaystyle ={B^{(\tau)}}^{\prime}[\Psi-\Sigma\lambda _{1}]-\delta_{1}^{\prime}$ (18)

when starting from $ A^{(0)}=0$ and $ B^{(0)}=0$. If bond prices are exponentially affine in the state variables then yields are affine in the state variables since $ P_{t}^{(\tau)}\!=\!\exp[-y_{t}^{(\tau)}\tau]$. Consequently, it follows that $ y_{t}^{(\tau)}=a^{(\tau)}+{b^{(\tau)}}^{\prime }Z_{t}$ with $ a^{(\tau)}=-A^{(\tau)}/\tau$ and $ b^{(\tau)}=-B^{(\tau)}/\tau$. To estimate the model we deviate from the popular Chen and Scott (1993) approach and instead assume that every yield is contaminated with measurement error in a state-space estimation set-up.

To summarize, we specify the following affine model

$\displaystyle y_{t}^{(\tau_{i})}$ $\displaystyle = a^{(\tau_{i})}+b^{(\tau_{i})} Z_{t}+\eps_{t}^{(\tau_{i})}$ (19)
$\displaystyle Z_{t}$ $\displaystyle =\mu+\Psi Z_{t-1}+u_{t}$ (20)
$\displaystyle \left[ \begin{array}[c]{c} \eps_{t}\\ u_{t} \end{array} \right]$ $\displaystyle \sim\mathcal{N}\bigg(\left[ \begin{array}[c]{c} 0_{13\times1}\\ 0_{3 \times1} \end{array} \right] , \left[ \begin{array}[c]{cc} H & 0\\ 0 & Q \end{array} \right] \bigg)$ (21)

where $ H$ is assumed to be a diagonal matrix, $ Q=\Sigma\Sigma^{\prime}$, and $ a^{(\tau_{i})}$ and $ b^{(\tau_{i})}$ are the recursive yield equation functions. We assume $ Z_{t}$ to consist of $ K=3$ common factors. We denote this model by ATSM.

We extend the model to incorporate observable macroeconomic factors in a similar way as for the Nelson-Siegel model,

$\displaystyle y_{t}^{(\tau_{i})}$ $\displaystyle = a^{(\tau_{i})}+b^{(\tau_{i})} f_{t}+\eps_{t}^{(\tau_{i})}$ (22)
$\displaystyle f_{t}$ $\displaystyle =\mu+\Psi f_{t-1}+\eta_{t}$ (23)
$\displaystyle \left[ \begin{array}[c]{c} \eps_{t}\\ \eta_{t} \end{array} \right]$ $\displaystyle \sim\mathcal{N}\bigg(\left[ \begin{array}[c]{c} 0_{13\times1}\\ 0_{12 \times1} \end{array} \right] , \left[ \begin{array}[c]{cc} H & 0\\ 0 & Q \end{array} \right] \bigg)$ (24)

with $ f_{t}=(Z_{t},M_{t},M_{t-1},M_{t-2})$. The state equation (23) is written in companion form and the dimensions of $ a^{(\tau_{i})}$, $ b^{(\tau_{i})}$, $ \mu$, $ \Psi$ and $ Q$ are again increased appropriately. As in the Nelson-Siegel model, $ Q$ is block diagonal with only two non-zero blocks, $ Q_{Z}$ and $ Q_{M}$. Unlike in the Nelson-Siegel model, however, in the affine model yield movements are also directly related to current and past macro movements through the bond pricing coefficients. We do assume that the short rate and risk premia only depend on contemporaneous values of the macro factors, i.e. we set all coefficients in $ \delta _{0},\delta_{1},\lambda_{0}$ and $ \lambda_{1}$ associated with $ M_{t-1}$ and $ M_{t-2}$ equal to zero, similar to the 'macro model' in Ang and Piazzesi (2003). We denote the affine model with macroeconomic factors by ATSM-X.

We want to note two points here. First, our affine-with-macro model is a hybrid between the macro model of Ang and Piazzesi (2003) and the FAVAR model of Monch (2008). Compared to Ang and Piazzesi (2003) we use macro factors that are based on many more macro variables, whereas compared to Monch (2008) we also incorporate latent yield factors. The yield factors are likely to improve the predictive ability of the model because the yield factors can better pick up high-frequency movements in yields (see also the discussion in Monch (2008)). Second, we estimate the affine model using the Kalman Filter where we assume that every yield has measurement error. This implies that the factors in $ f_{t}$ are not simply a linear combination of yields so that the macro factors do truly add exogenous information to the model.

Adding macroeconomic variables or factors to affine models can cause estimation problems because it further increases the number of parameters in these already highly parameterized models.13 To speed ups as well as to facilitate the estimation procedure, we therefore use the two-step approach of Ang, Piazzesi, and Wei (2006) by making the latent yield factors observable. Contrary to Ang, Piazzesi, and Wei (2006), however, who directly use the observed short rate and the term-spread as measures of the level and slope of the yield curve, we use principal component analysis to extract common factors from the full set of yields. We use the first three factors as our observable state variables.

4  Forecasting

4.1  Forecast Procedure

We divide our dataset into an initial estimation sample which covers the period 1970:1 - 1988:12 (228 observations) and a forecasting sample which is comprised of the remaining period 1989:1 - 2003:12 (180 observations). The first sixty months of the forecast period are used as a training sample to start up the forecast combinations discussed in Section 5. Consequently, we report forecast results for the sample 1994:1 - 2003:12 (120 observations).

We recursively estimate models using an expanding window, starting from the initial sample 1970:1 - 1988:12.14 Given a set of parameter estimates, we construct point forecasts for four different horizons: $ h=1, 3, 6$ and 12 months ahead. As discussed in the previous section, for horizons beyond $ h=1$ month we compute iterated forecasts. To prevent data-snooping, we also recursively construct the macroeconomic factors (see Section 2.2), as well as the yield curve factors used in the VAR and the ATSM.

4.2  Forecast Evaluation

To evaluate out-of-sample forecasts we compute popular error metrics, per maturity and per forecast horizon. For a full sample evaluation we compute the Root Mean Squared Prediction Error (RMSPE). Similar to Hordahl, Tristani, and Vestin (2006) we also summarize the forecasting performance of each model across all maturities for a given forecast horizon by computing the Trace Root Mean Squared Prediction Error (TRMSPE), see Christoffersen and Diebold (1998) for details.

The drawback of using (T)RMSPE statistics is, however, that these are single statistics summarizing individual forecasting errors over an entire sample. Although often used, unfortunately they do not give any insight as to where in the sample models make their largest and smallest forecast errors. We therefore also graphically analyze the Cumulative Squared Prediction Errors (CSPE) used in Welch and Goyal (2008). These cumulative squared prediction error series clearly show in which months models outperform and in which months they underperform a given benchmark (here the random walk model). The model-$ m$, time-$ T$ CSPE for a $ \tau_{i}$-month maturity is given by

CSPE$\displaystyle _{m,T}(\tau_{i})=\sum_{t=1}^{T}\left[ \left( \widehat{y} _{t+h\vert t,\text{RW}}^{(\tau_{i})}-y_{t+h}^{(\tau_{i})} \right) ^{2} - \left( \widehat{y}_{t+h\vert t,m}^{(\tau_{i})}-y_{t+h}^{(\tau_{i})} \right) ^{2}\right]$ (25)

where $ y_{t+h}^{(\tau_{i})}$ is the yield for a $ \tau_{i}$-month maturity observed at time $ t+h$, while $ \widehat{y}_{t+h\vert t,m}^{(\tau_{i})}$ is its model-$ m$ forecast, made at time $ t$. See Appendix B for further detailed formulas.

To test for statistically significant differences in forecasting accuracy between competing models we apply the Model Confidence Set (MCS) approach developed by Hansen, Lunde, and Nason (2003), Hansen, Lunde, and Nason (2005). Given a set of competing forecasting models, $ M_{0}$, the MCS procedure identifies the MCS $ \widehat{M}_{\alpha}^{*}\subset M_{0}$, which is the set of models that contains the "best" forecasting model given a confidence level $ 1-\alpha$. Starting from the full set of models, $ M=M_{0}$, and a vector of $ R$ forecasts, the MCS procedure repeatedly tests the null hypothesis of equal forecasting accuracy,

$\displaystyle H_{0,M}: E[d_{ij,t}]=0,\;$   for all $\displaystyle \, i,j \in M, $

where $ d_{ij,t}=L_{i,t}-L_{j,t}$ is the loss differential between models $ i$ and $ j$ in the set, with $ L$ being an appropriate loss function. The MCS procedure sequentially eliminates the worst performing models from $ M$ as long as the null is rejected. This procedure is repeated until the null is no longer rejected, in which case the surviving set is $ \widehat{M}_{\alpha}^{*} $. We follow Hansen, Lunde, and Nason (2003) by using their semi-quadratic statistic which gives the following $ t-$ statistics:

$\displaystyle T_{SQ}\equiv\sum_{i,j\subset M}t_{ij}^{2}, $

where $ t_{ij}=\frac{\overline{d}_{ij}} {\sqrt{\widehat{var}(\overline{d} _{ij})}}$ for $ i,\,j\subset M$ and $ \overline{d}_{ij}=\frac{1}{R}\sum _{t=T}^{T+R-1}d_{ij,t}$. Similarly, we implement the MCS procedure using the stationary block bootstrap of Politis and Romano (1994) with an average block length of 20 months and we the squared forecast error as loss function.

In the tables below we report results for confidence levels of $ 1-\alpha=90\%$ and $ 1-\alpha=75\%$. The test is performed independently for different maturities and forecast horizons.

4.3  Forecasting Results: Individual Models

We start our discussion of the forecasting performance of individual models by considering the results in Panels A and B of Tables 3 to 6. The first row of each table reports the (T)RMSPE for the random walk model, whereas the remaining rows in Panels A and B are (T)RMSPEs relative to those of the random walk. Any number below one therefore indicates outperformance relative to the random walk, whereas any number larger than one signals underperformance. Two stars next to the RSMPE individual models indicates that a model belongs to the model set $ \widehat{\mathcal{M}}^{*}_{0.25}$ according to the $ T_{SQ}$ test statistic, whereas one star is for when it belongs to the model set $ \widehat{\mathcal{M} }^{*}_{0.10}$ instead. Figures 12 to 15 show time-series plots of the realized and predicted yields, both for individual models as well as for forecast combination methods (discussed in Section 5).

At first sight the results in Tables 3 to 6 are disappointing if we focus solely on the TRMSPE results in the first column of each table. There is not a single model that, across the board of maturities, consistently outperforms the random walk for all forecast horizons, as reflected by the relative TRMSPE statistics. In addition, when considering each horizon in isolation, still only a few models produce forecasts which are more accurate than simply repeating the last known value, and for those that do the improvements are often only marginal. The univariate autoregressive model augmented with macro factors gives the lowest TRMSPE for short horizons (1 and 3 months), whereas the VAR model with macro factors does so for longer horizons (6 and 12 months). More complex models such as the affine and Nelson-Siegel models perform poorly.

Focusing on specific maturities gives us more and different insights however. Predictability tends to be relatively high for short forecast horizons and short maturities as evident from the relative RMSPE statistics. For example, for the 1-month yield the majority of models outperform the random walk at both the 1-month and 3-month forecast horizon. Moreover, for both horizons the random walk is not in the final full-sample Model Confidence Set. For medium maturities, such as the 1-year and 2-year yield, the random walk is more difficult to beat, although the MCS tends to be smallest for these yields, consisting primarily of the random walk and the AR-X model. Although some models still provide RMSPE statistics below one for long maturities, only a few models, if any, are dropped from the final MCS. For example, for the 10-year yield all models end up in the MCS at the 3-month horizon.

For the 6-month and 12-month forecast horizons, using macroeconomic information seems to be a pre-requisite for obtaining at least some level of predictability. Among the macro-augmented yield models, the VAR-X model outperforms the random walk most consistently across maturities, in particular for a 12-month horizon. Contrary to its results for shorter forecast horizons, the AR-X model is now accurate only for short maturities. Interestingly, the most accurate forecasting models for short maturities are the NS1-X and ATSM-X models. For medium and longer-dated maturities, imposing no-arbitrage restrictions on factor loadings does not help in forecasting yields. This result is consistent with Duffee (2009) who argues that no-arbitrage restrictions have no practical effect on forecast accuracy.

With the exception of one case - the ATSM for the 1-month yield for a 6-month forecast horizon - not a single yield-only model outperforms the random walk. Despite this, however, it proves to be very difficult to eliminate these models from the final Model Confidence Set. Only in rare occasions do models get discarded, indicating a substantial degree of model uncertainty. A final interesting observation to make from Tables 3 to 6 is that the two-step Nelson-Siegel models, regardless of whether these incorporate macroeconomic information or not, perform poorly across maturities and forecast horizons. This appears to contradict the results of Diebold and Li (2006) who find that the Nelson-Siegel model, especially the NS2-AR model, forecasts particularly well during the 1994-2000 period. As we will show below, the Nelson-Siegel model turns out to be one of the most prominent examples of the extent to which the forecast accuracy of term structure models can vary over time.

To further gauge the degree of model uncertainty, we analyze Cumulative Squared Prediction Error graphs. Because we construct forecasts for the entire sample period 1989 - 2003, we first take a step back and discuss results for the entire fifteen-year out-of-sample forecast period. The reason for doing this is that it also allows us to analyze our five-year training period. We feel this is interesting because it can give us some insights in the initial forecast combination weights, but more importantly, because the training period contains the 1990-1991 recession. Figures 4 to 7 show CSPEs for yield-only and macro models separately for each forecast horizon.15 Each line in the graph represents a different model and shows how that particular model performs relative to the random walk benchmark. In particular, an increasing CSPE indicates outperformance whereas a decreasing CSPE indicates that the random walk is making smaller forecasting errors.

As shown by the yellow bars in Figures 4 to 7, our out-of-sample period contains two NBER recessions. Both these recessions are characterized by a steep decline in short term interest rates as the Fed lowered its target interest rate, and by a sharp increase in the spread between long and short rates, see Figure 1(b). As it is also evident from earlier recessions, shown in Figure 1(a), spreads tend to remain high for quite a while until the Fed starts to raise short term interest rates again. The period in between the 1990-1991 and 2001 recessions, in particular the period 1994-2000, looks quite different on the other hand with much more stable interest rate dynamics, and seems best described as a low-volatility, low-spread regime for interest rates. Interestingly, Duffee (2002), Ang and Piazzesi (2003), and Diebold and Li (2006), among others, all tend to report a fair amount of predictability for this period. The CSPE graphs allow us to examine in much more detail how models perform during this period as well as during both recession periods, virtually on a month-to-month basis. Similar to us, Monch (2008) and Carriero, Kapetanios, and Marcellino (2009) compare the forecast performance of a range of different models. They find that their preferred FAVAR and BVAR model, respectively, have the best relative RSME performance. To check the robustness of this result, they perform subsample analysis. However, both studies do so by considering just two subsamples, so we can still only judge models based on a single summary statistic for each subsample. This again does not give any real insight into where and why models perform well or not.

Although our out-of-sample period only contains two recessions, we believe the CSPE graphs reveal four important features. First, macro models perform better just prior to and during recessions. The CSPE lines are increasing in those periods, indicating that macro models forecast more accurately than the random walk. This is particularly true for long forecast horizons, see for example Figure 7. As several macro models simultaneously outperform the random walk, it clearly is the case that it is the macroeconomic information that is driving this result, and not so much any specific model. Ludvigson and Ng (2009) offer an interesting insight which can explain why macro information is useful in and around recessions. They find that macro factors explain risk premia much more than yield information does. Furthermore, they show that during recessions risk premia account for the largest portion of yield levels, implying that macro models will be better capable of forecasting the direction of yields in and around recessions. This certainly seems to be the case judging from Figures 4 to 7.

Second, most models perform poorly when the spread between long and short interest rates is high, after rates have begun to stabilize, but with medium-maturity yields being closer to short than they are to long rates. This is a typical shape of the term structure one or two years after recessions, in our case 1992-1993 and 2003. Only the AR-X models seems capable of coping this situation. Multivariate models all struggle in these periods. This is perhaps due to the fact that the larger number of estimated model parameters result leads to a less accurate fit of the term structure during these periods, which in turn is likely to lead to poor forecasts. Favero, Niu, and Sala (2009) offer some interesting insights on the role of estimation error on the forecasting performance of affine models, especially for longer-maturity yields. See also Duffee (2009) for comments on the numerical instability of affine models.

Third, yield-only models perform well in expansionary periods such as 1994-1998, corroborating the results in the above-mentioned studies, but very poorly in and around recession periods.

Fourth, and this is our most important point, there is not a single model that clearly performs well across all maturities and forecast horizons. Hence there is a substantial degree of model uncertainty. Believing in any single model all the time can give very accurate forecasts in one period but, more troublesome, potentially very poor forecasts in other periods. Probably the best example of this is the Diebold and Li (2006) NS2-AR model. Figures 4 to 7 confirm the Diebold and Li (2006) results that the NS2-AR model gives very accurate forecasts for the period from 1994 to 2000, especially for longer forecast horizons. However, the CSPE graphs also show that most, if not all, of these forecast gains are confined to 1994 and 1995 when the NS2-AR model is by far the best performing model. During the years after 1995, the CSPE lines are all but flat, indicating that NS2-AR forecasts are about as accurate as the random walk model. Immediately following both the 1991 and 2001 recession, the NS2-AR performs by far the worst out of all models, as evidenced by the precipitous drop in CSPEs. All in all, the NS2-AR model is a prime example of the degree to which the forecast accuracy of term structure models can vary over time. Monch (2008) also notes that "$ \dots$ some of the strong forecast performance of the Nelson-Siegel model documented by Diebold and Li may be due to their choice of forecast period."

Because in the end our main focus is on the 1994-2003 out-of-sample period, we show CSPEs in Figure 8 to 11 for the 1994-2003 period in the left-hand side and middle panels for individual models. These graphs therefore cover the same period as in Tables 3-6 and exclude the 1991 recession.16 In the next section we will confront these graphs with CSPE graphs based on forecast combinations, the right-hand side panels.

5  Forecast Combination

Our cumulative squared prediction error analysis reveals that it is seems virtually impossible to identify a single model that consistently outperforms the random walk for an entire out-of-sample period. The forecasting ability of individual models clearly varies over time considerably. Each model appears to play a complementary role in approximating the data generating process, at least during subperiods. Model uncertainty is troublesome if one has hopes of obtaining a single model for forecasting. A worthwhile endeavor for cushioning the effects of model uncertainty is to combine the forecasts of different models, see Timmermann (2006) for a recent survey. For example, one "solution" as to whether to impose no-arbitrage restrictions or not is to simply combine the forecasts from no-arbitrage models with those from unrestricted models. In this section we therefore examine several forecast combination schemes. Two combination methods are standard approaches which combine forecasts from all available models. In the third scheme we first filter out the worst-performing individual models before combining the forecasts from the remaining models. Below, we first discuss the different schemes. We then examine the forecast combination results and compare these with the single-model results for the 1994 - 2003 out-of-sample period.

5.1  Forecast Combination Schemes

Assuming we are combining forecasts from $ M$ different forecast models, a combined forecast for a $ h$-month horizon for the yield with maturity $ \tau_{i}$ is given by $ \widehat{y}_{T+h\vert T}^{(\tau_{i})}=\sum_{m=1} ^{M}w_{T+h\vert T,m}^{(\tau_{i})}\widehat{y}_{T+h\vert T,m}^{(\tau_{i})}$ , where $ w_{T+h\vert T,m}^{(\tau_{i})}$ denotes the weight assigned to the time-$ T$ forecast from the $ m^{\text{th}}$ model; $ \widehat{y}_{T+h\vert T,m}^{(\tau_{i})}$.

Scheme 1: Equally Weighted Forecasts

The first forecast combination method we consider assigns equal weights to the forecasts from all individual models, i.e. $ w_{T+h\vert T,m}^{(\tau_{i})}=1/M$ for $ m=1,\ldots,M$. We denote the resulting combined forecast as Forecast Combination - Equally Weighted (FC-EW). As explained in Timmermann (2006), this approach is likely to work well if forecast errors from different models have similar variances and are highly correlated. Unreported statistics confirm that forecast errors from the individual models are indeed highly correlated here and have high variance.

Scheme 2: Inverted MSPE-Weighted Forecasts

The second forecast combination scheme we examine uses weights which are based on relative historical performance. More specifically, model weights are based on each model's (inverted) MSPE, relative to those of all other models, computed over a window of the previous $ \upsilon$ months. We denote these performance-based combinations forecasts by Forecast Combination - MSPE (FC-MSPE).17 The weight for model $ m$ is computed as $ {w}_{T+h\vert T,m}^{(\tau_{i} )}=\frac{1/\text{MSPE}_{h\vert T,m}^{(\tau_{i})}}{\sum_{m=1}^{M}(1/\text{MSPE} _{h\vert T,m}^{(\tau_{i})})}$ where MSPE$ _{h\vert T,m}^{(\tau_{i})}\!=\!\frac {1}{\upsilon}\sum_{r=1}^{\upsilon}(\widehat{y}_{T-r+1\vert T-h-r+1,m}^{(\tau_{i} )}-y_{T-r+1}^{(\tau_{i})})^{2}$ . A model with a lower MSPE is given a relatively larger weight than a worse performing model, see Timmermann (2006) for a discussion and Stock and Watson (2004) for an application to forecasting GDP growth. The weights applied in this and the previous forecast combination scheme are always bounded between 0 and 1. Other approaches for which this does not necessarily need to be the case, in particular OLS-based weights (see again Timmermann (2006)), proved to be problematic here due to multicollinearity problems among the different forecasts. This resulted in often extreme (offsetting) weights and we therefore decided not to further pursue these approaches.

The number that should be used for $ \upsilon$ is difficult to determine a priori. Using a smaller window will make weights more responsive to changes in models' forecasting accuracy, but at the same time it will also tend to make them more noisy. The optimal choice of $ \upsilon$ will therefore need to be determined empirically. Somewhat counterintuitive maybe, we found that using an expanding window approach works the best. We tried different lengths in a moving window approach (in particular, $ \upsilon=12$, 24 and 60 months) but for shorter windows results were (marginally) worse. Similarly, a weighted approach using declining weights for older forecast errors as in Diebold and Pauly (1987) also gave worse results. We settled on using an expanding window, whose length is initially set to $ \upsilon=60$ months but which increases with every new yield realization that becomes available.

Finally, for Scheme 1 and 2 we distinguish between using forecasts of macro models only; FC-EW-X and FC-MSPE-X, and combining forecasts across all models; FC-EW-ALL and FC-MSPE-ALL.

Scheme 3: Trimming Via Model Confidence Set

The Model Confidence Set approach for evaluating forecast performance, as described in Section 4, can also be implemented as an initial model elimination mechanism. The idea of trimming the available set of models prior to combining forecasts has been proposed in several studies, see for example Timmermann (2006). As these studies show, trimming is an efficient way to first discard of the "worst" models, and then combine the forecasts from the surviving models. The MCS approach seems particularly suitable for doing so because it requires few a priori decisions, such as for example having to select the number of remaining models. As the MCS grows and shrinks over time, so does the number of models whose forecasts are combined into a single number.

As our third and final forecast combination scheme we therefore combine forecasts from models that survive the MCS approach, using equal and MSPE-based weights. Specifically, in order to construct a $ h$-month ahead combination forecast at time $ T$, we use the $ T_{SQ}$ statistic to construct $ \widehat{\mathcal{M}}^{*}_{0.25}$, using a confidence level of $ 1-\alpha= 75\%$.18 We determine $ \widehat{\mathcal{M}}^{*}_{0.25}$ using an expanding window of previous forecasts, starting from the initial sixty-month sample 1989:1 - 1993:12. To determine the MCS we always start by inserting all available individual models, i.e. the entire set $ M_{0}$, so as not to have to make a (subjective) initial model selection.

By studying which models are contained in $ \widehat{\mathcal{M}}^{*}_{0.25}$ over time we can also again infer information about the consistency of models' forecasting performance. In Tables 3 to 6 we therefore also report the percentage of times each individual model is included in the model confidence sets for the 1994:1 - 2003:12 sample (in parentheses below each (relative) (T)RMSPE statistic). For example, a number close to one indicates that a model is nearly always included in the combination set, whereas a number close or equal to zero shows that it is typically excluded.19

5.2  Forecast Combination Results

We feel that there are at least three important conclusions that we can draw from the forecast combination results in Tables 3-6 and Figures 8 to 11. First, several forecast combination schemes perform better or similar to the random walk across different forecast horizons. TRMSPEs and RMSPEs are often below one, albeit marginally in some cases. Compared to the best performing individual models, prediction errors for the forecast combination schemes are somewhat higher, but they certainly seem to be more stable, as is evident from the right-hand side panels in Figures 8 to 11, even though it may not be initially clear from Figures 12 to 15. Focusing on Figures 8 to 11, the performance variability associated with macro models is reduced substantially in the first part of the sample and the bad performance of yield-only models during and after the 2001 recession is mitigated.

Second, averaging across all the models, after trimming out the worst performing ones using the MCS approach, gives the best performance for shorter forecast horizons (the bottom two lines in the tables). The gains are particular encouraging for shorter maturities. The inclusion percentages (in parentheses in the tables) reveal that this trimming-via-MCS scheme nearly always select the best performing individual models in the forecast combination. For example, with a 1-month horizon for the 1-month maturity, the VAR, VAR-X, ATSM, ATSM-X, and the NS2-VAR-X models, are basically always included. In other cases, such as for example for the same horizon but now for the 1-year maturity, only a single model (AR-X) actually makes it into the MCS. The differences between using equal and MSPE weights are minor, enforcing the conclusion that it is the trimming procedure which is most beneficial to the forecast combination method, not so much which weights are used to sum the individual forecasts. The light-blue lines in Figures 8 and 9 show that the FC-MCS-EW scheme does not always necessarily provide the best forecasts, but it certainly produces much less prediction error volatility.

Third, averaging only across macro models produces the most accurate forecasts for longer horizons. The MCS inclusion percentages indicate that it is very difficult to discard models and many specifications indeed have high inclusion percentages. However, combining forecasts of macro models only, lines 4 in Panel C in each table, gives RMSPE ratios which are almost always below one, in particular for the twelve-month horizon. The FC-MSPE-X scheme appears to be the best forecasting strategy. Figures 10 and 11 reveal that that is in part due to the fact that the FC-MSPE-X performs best during and after the 2001 recession. Nevertheless, the results suggest that the past performance of individual models provides a useful insight as to which models to include in the forecast combination. Going back to Table 6, the FC-MSPE-X scheme does particularly well across maturities for the twelve-month horizon but, quite important, especially for longer-dated maturities. Earlier studies with individual models tend to find that it is typically very hard to accurately forecast long-term rates and our results in Panel A and B confirm this. The outperformance of the FC-MSPE-X scheme relative to the random walk is 8% for the ten-year maturity whereas the best individual model (AR-X) is only barely below one. This result suggest that forecasting combinations can potentially be very useful for forecasting long-maturity yields with long forecast horizons.

6  Conclusion

This paper addresses the task of forecasting the term structure of interest rates. Several recent studies have shown that significant steps forward are being made in this area. We contribute to the existing literature by further assessing the importance of incorporating macroeconomic information, and, in particular, by examining model uncertainty. Our results show that incorporating macroeconomic information indeed helps to improve forecasts of individual models. Our main result, however, is that the predictive performance of individual models can be strongly time-varying, which makes putting all one's eggs in a single model basket risky. Our suggested alternative, combining forecasts across different models, not only mitigates model uncertainty, but also results in accurate forecasts.

We have examined the forecast accuracy of a range of models with varying degrees of complexity. We showed that the predictive ability of individual models varies over time considerably. Models that incorporate macroeconomic variables are more accurate during interest rate regimes where the uncertainty about the future path of interest rates is substantial. As an example we mention the period during and after the 2001 recession. Models without macro information do particularly well in subperiods where the term structure has a more stable pattern (such as in the late 1990s) or when the spread between long and short-maturity yield closes.

The fact that different models forecast well in different subperiods confirms ex-post that alternative model specifications play a complementary role in approximating the data generating process. We believe our results provide a strong claim for using forecast combination techniques as an alternative to believing in a single model. We show that combining forecasts of all individual models with and without macro factors, after trimming out the worst performing models using the Model Confidence Set approach, gives accurate forecasts for short forecast horizons. Combination forecasting of models with macro information, using a weighting method that is based on relative historical performance over a long sample, results in superior forecasts for long forecast horizons. The gains in the latter case are particularly encouraging for longer-dated maturities, which have proven to be notoriously difficult to predict.

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A  Individual Interest Rate Models

In this appendix we provide some further details on how we perform inference on the parameters of each of the models in Section 3.

A.1  AR Model

We estimate the parameters $ \{c^{(\tau_{i})}, \phi^{(\tau_{i})}, \psi ^{(\tau_{i})}\}$ using standard ordinary least squares (OLS). Given the parameter estimates, we construct iterated forecasts as

$\displaystyle \widehat{y}_{T+h}^{(\tau_{i})}=\hat{c}^{(\tau_{i})} +\hat{\phi}^{(\tau_{i})}\widehat{y}_{T+h-1}^{(\tau_{i})}+{\hat{\psi}} ^{(\tau_{i})^{\prime}}\widehat{X}_{T+h}$ (A-1)

with $ \widehat{y}_{T}^{(\tau_{i})}=y_{T}^{(\tau_{i})}$. We construct forecasts from the AR model both with and without macroeconomic factors. The macro factor forecasts, $ \widehat{X}_{T+h}$, are iterated forecasts constructed from the VAR(3) macro factor model.

A.2  VAR Model

We estimate the equation parameters $ \{c, \Phi, \Psi\}$ in (5) using equation-by-equation OLS as each equation has an identical set of regressors. We construct forecasts as follows:

$\displaystyle \widehat{Y}_{T+h}=\widehat{c}+\widehat{\Phi}\widehat{F}_{T+h-1}+\widehat{\Psi }\widehat{X}_{T+h}$ (A-2)

where we compute the yield factor forecasts, $ \widehat{F}_{T+h-1}$, by first calculating the principal component factor loadings using data only up until month $ T$ and then multiplying these loadings with the iterated yields forecasts.

A.3  Nelson-Siegel Model

We estimate the Nelson-Siegel model with the two-step approach of Diebold and Li (2006) as well as the one-step approach of Diebold, Rudebusch, and Aruoba (2006).

In the two-step approach we fix $ \lambda$ to 16.42, which, as shown in Diebold and Li (2006), maximizes the curvature factor loading at a 30-month maturity. Given the value for $ \lambda$ we then estimate the vector of latent factors for every individual month by applying OLS to the cross-section of yields (all 18 maturities). From this first step we obtain time-series for the three factors, $ \{\beta_{t}\}_{t=1}^{T}$. The second step consists of estimating the dynamics of the factors in (7) by either fitting a single VAR(1) model, or by separate AR(1) models.

In the one-step approach we estimate the unknown parameters and latent factors by means of the Kalman Filter. We maximize the likelihood using the prediction error decomposition of the state space model in (6) and (7). For each sample in the recursive estimation procedure, we first run the two-step approach with a VAR(1) specification for the state vector to obtain starting values. The unconditional mean and covariance matrix of $ \{\beta_{t}\}_{t=1}^{T}$ are used to start the Kalman Filter. We discard the first 12 observations when evaluating the likelihood. All variance parameters of the diagonal matrix $ H$ and the full matrix $ Q$ are initialized to 1. The covariance terms in $ Q$ are initialized to 0. In the optimization procedure, we maximize the likelihood by treating the standard deviations as parameters instead of optimizing over the variance parameters directly, to ensure that all variance parameters are positive. We initialize $ \lambda$ to 16.42.

We obtain iterated forecasts for the factors as follows:

$\displaystyle \widehat{f}_{T+h}=\widehat{a}+\widehat{\Gamma}\widehat{f}_{T+h-1}$ (A-3)

where $ \widehat{f}_{T+h}=(\widehat{\beta}_{1,T+h},\widehat{\beta} _{2,T+h},\widehat{\beta}_{3,T+h})^{\prime}$ for the model without macro factors, whereas $ \widehat{f}_{T+h}=(\widehat{\beta}_{1,T+h},\widehat{\beta }_{2,T+h},$
$ \widehat{\beta}_{3,T+h},\widehat{M}_{T+h}, \widehat{M} _{T+h-1},\widehat{M}_{T+h-2})^{\prime}$ when macro factors are included. The factor forecasts are then inserted in the measurement equation to compute interest rate forecasts:

$\displaystyle \widehat{y}_{T+h}^{(\tau_{i})} \!=\! \widehat{\beta}_{1,T+h} + \widehat{\beta }_{2,T+h} \left( \frac{1\!-\!\exp(-\tau_{i}/\widehat{\lambda})}{\tau _{i}/\widehat{\lambda}} \right) + \widehat{\beta}_{3,T+h} \left( \frac{1\!-\!\exp(-\tau_{i}/\widehat{\lambda})}{\tau_{i}/\widehat{\lambda}}\! -\! \exp(-\tau_{i}/\widehat{\lambda}) \right)$ (A-4)

A.4  Affine Model

To estimate the affine model we assume that every yield is contaminated with measurement error. We estimate the parameters in the resulting state space model by applying the two-step approach used in Ang, Piazzesi, and Wei (2006). We make the latent factors $ Z_{t}$ observable by extracting the first three principal components from the panel of yields. The first step of the estimation procedure consists of estimating the equation and variance parameters of the state equations in (23). In the second step we estimate the remaining parameters $ \{\delta_{0}, \delta_{1}, \lambda_{0}, \lambda_{1}\}$. We first estimate $ \{\delta_{0}, \delta_{1}\}$ by applying OLS to the short rate equation (13) where we use the 1-month yield as the observable short rate. We then estimate the risk premia parameters $ \{\lambda_{0},\lambda_{1}\}$ by minimizing the sum of squared yields errors, taking as given the parameter estimates from the first step, $ \{\widehat{\mu}$, $ \widehat{\Psi}, \widehat{\Sigma}\}$ and the short rate parameters $ \{\widehat{\delta}_{0}, \widehat{\delta}_{1}\}$. When we optimize over the risk premium parameters in the second step, we initialize all risk premia parameters with zeros. Common approaches for obtaining starting values for the risk premia parameters which tend to first estimate either $ \lambda_{0}$ or $ \lambda_{1}$ in a separate step, gave unsatisfactory results. So we decided to initialize the optimization procedure assuming that all risk premium parameters are zero. We incorporate macro factors by writing the state equations in companion form. All parameters in the short rate equations and the time-varying risk premia that are associated with lags of the macro factors are set to zero.

Yield forecasts are generated by forward iteration of the state equations:

$\displaystyle \widehat{f}_{T+h}=\widehat{\mu}+\widehat{\Psi}\widehat{f}_{T+h-1}$ (A-5)

where $ \widehat{f}_{T+h}=\widehat{Z}_{T+h}$ for the yields-only model whereas $ \widehat{f}_{T+h}=(\widehat{Z}_{T+h}, \widehat{M}_{T+h-1},\widehat{M} _{T+h-2})$ for the affine model with macro factors.

With the estimated parameters substituted in the recursive bond pricing coefficient equations $ a^{(\tau_{i})}$ and $ b^{(\tau_{i})}$, we then construct interest rate forecasts as

$\displaystyle \widehat{y}_{T+h}^{(\tau_{i})} = \widehat{a}^{(\tau_{i})}+\widehat{b} ^{(\tau_{i})}\widehat{f}_{T+h}$ (A-6)

B  Forecast Evaluation Criteria

In the tables below we report the (Trace) Root Mean Squared Prediction Errors. Given a sample of $ R$ out-of-sample forecasts with a $ h-$month ahead forecast horizon, we compute the RMSPE for a $ \tau_{i}$-month yield for model $ m$, with $ m=1,\ldots,M$, as follows:

RMSPE$\displaystyle _{m}(\tau_{i})=\sqrt{\frac{1}{R}\sum_{t=1}^{R}\left( \widehat{y}_{t+h\vert t,m}^{(\tau_{i})}-y_{t+h}^{(\tau_{i})} \right) ^{2}}$ (B-1)

where $ y_{t+h}^{(\tau_{i})}$ is the yield for a $ \tau_{i}$-month maturity observed at time $ t+h$, while $ \widehat{y}_{t+h\vert t,m}^{(\tau_{i})}$ is its model-$ m$ forecast, made at time $ t$.

The TRMSPE is an aggregate over all $ N$ yield maturities:

TRMSPE$\displaystyle _{m}=\sqrt{\frac{1}{N}\frac{1}{R}\sum_{i=1}^{N}\sum_{t=1} ^{R}\left( \widehat{y}_{t+h\vert t}^{(\tau_{i})}-y_{t+h}^{(\tau_{i})} \right) ^{2} }\qquad\quad$ (B-2)

The Cumulative Squared Prediction Error (CSPE) computes the sum of squared prediction errors for a model $ m$, relative to those of a benchmark model, here the random walk (RW):

CSPE$\displaystyle _{m,T}(\tau_{i})=\sum_{t=1}^{T}\left[ \left( \widehat{y} _{t+h\vert t,\text{RW}}^{(\tau_{i})}-y_{t+h}^{(\tau_{i})} \right) ^{2} - \left( \widehat{y}_{t+h\vert t,m}^{(\tau_{i})}-y_{t+h}^{(\tau_{i})} \right) ^{2}\right]$ (B-3)

If a model outperforms the random walk, then CSPE$ _{m,T}$ will be an increasing series. If the random walk produces more accurate forecasts, then CSPE$ _{m,T}$ will tend to be decreasing. The CSPE is informative at each point in time basically, as it will go up in any given month if the model outperforms its benchmark, whereas it will go down vice versa.

Table 1. Summary Statistics

 maturity  mean   stdev   skew   kurt   min   max   JB  ρ1ρ12ρ24
 1-month  6.049   2.797   0.913   4.336   0.794   16.162   85.671   0.968   0.690   0.402  
 3-month  6.334   2.896   0.871   4.237   0.876   16.020   76.380   0.974   0.708   0.415  
 6-month  6.543   2.927   0.788   4.016   0.958   16.481   58.796   0.976   0.723   0.444  
 1-year   6.755   2.860   0.661   3.763   1.040   15.822   38.907   0.975   0.733   0.474  
 2-year   7.032   2.724   0.644   3.672   1.299   15.650   35.240   0.978   0.748   0.526  
 3-year   7.233   2.594   0.685   3.663   1.618   15.765   38.796   0.979   0.763   0.560  
 4-year   7.392   2.510   0.728   3.607   1.999   15.821   41.640   0.980   0.771   0.582  
 5-year   7.483   2.449   0.759   3.478   2.351   15.005   42.454   0.982   0.786   0.607  
 6-year   7.611   2.406   0.791   3.437   2.663   14.979   45.236   0.983   0.797   0.626  
 7-year   7.659   2.344   0.841   3.488   3.003   14.975   51.562   0.983   0.787   0.623  
 8-year   7.728   2.320   0.841   3.365   3.221   14.936   49.798   0.984   0.809   0.651  
 9-year   7.767   2.317   0.877   3.427   3.389   15.018   54.765   0.985   0.813   0.656  
 10-year  7.745   2.266   0.888   3.496   3.483   14.925   57.117   0.985   0.796   0.647  

Notes: The table shows summary statistics for our sample of end-of-month continuously compounded U.S. zero-coupon yields. Reported are the mean, standard deviation, skewness, kurtosis, minimum, maximum, the Jarque-Bera test statistic for normality and the 1st, 12th and 24th sample autocorrelation. The results shown are for annualized yields (in percentage points). The sample period is January 1970 - December 2003 (408 monthly observations).

Table 2a. Macroeconomic Dataset - Real Output and Income

Group (Code)
Transformation Code
Description
1
7
Personal Income (B$, Chain 2000)
1
7
Personal Income Less Transfer Payments (B$, Chain 2000)
1
7
Industrial Production Index - Total Index
1
7
Industrial Production Index - Products, Total
1
7
Industrial Production Index - Final Products
1
7
Industrial Production Index - Consumer Goods
1
7
Industrial Production Index - Durable Consumer Goods
1
7
Industrial Production Index - Nondurable Consumer Goods
1
7
Industrial Production Index - Business Equipment
1
7
Industrial Production Index - Materials
1
7
Industrial Production Index - Durable Goods Materials
1
7
Industrial Production Index - Nondurable Goods Materials
1
7
Industrial Production Index - Manufacturing
1
7
Industrial Production Index - Residential Utilities
1
7
Industrial Production Index - Fuels
1
1
NAPM Production Index (percent)
1
8
Manufacturing Capacity Utilization

Table 2b. Macroeconomic Dataset - Employment and Hours

Group (Code)Transformation CodeDescription
 2    1    Index of Help-Wanted Advertising In Newspapers (1967=100, SA)  
 2    1    Employment Ratio of Help-Wanted Ads to No. of Unemployed in Civilian Labor Force  
 2    7    Civilian Labor Force: Employed, Total (Thousands, SA)  
 2    7    Civilian Labor Force: Employed, Nonagricultural Industries (Thousands, SA)  
 2    1    Unemployment Rate: All Workers, 16 Years & Over (percent,Sa)  
 2    8    Unemployment by Duration: Average (Mean) Duration In Weeks (SA)  
 2    7    Unemployment by Duration: Persons Unempl.Less Than 5 Weeks (Thousands, SA)  
 2    7    Unemployment by Duration: Persons Unemployment 5 To 14 Weeks (Thousands, SA)  
 2    7    Unemployment by Duration: Persons Unemployment 15 Weeks or more (Thousands, SA)  
 2    7    Unemployment by Duration: Persons Unemployment 15 To 26 Weeks (Thousands, SA)  
 2    7    Unemployment by Duration: Persons Unemployment 27 Weeks or more (Thousands, SA)  
 2    7    Average Weekly Initial Claims, Unemployment Insurance (Thousands)  
 2    7    Employees on Nonfarm Payrolls: Total Private  
 2    7    Employees on Nonfarm Payrolls -Goods-Producing  
 2    7    Employees on Nonfarm Payrolls -Mining  
 2    7    Employees on Nonfarm Payrolls -Construction  
 2    7    Employees on Nonfarm Payrolls -Manufacturing  
 2    7    Employees on Nonfarm Payrolls -Durable Goods  
 2    7    Employees on Nonfarm Payrolls -Nondurable Goods  
 2    7    Employees on Nonfarm Payrolls -Service-Providing  
 2    7    Employees on Nonfarm Payrolls -Trade, Transportation, And Utilities  
 2    7    Employees on Nonfarm Payrolls -Wholesale Trade  
 2    7    Employees on Nonfarm Payrolls -Retail Trade  
 2    7    Employees on Nonfarm Payrolls -Financial Activities  
 2    7    Employees on Nonfarm Payrolls -Government  
 2    7    Employee Hours in Nonagricultural Establishments (B. Hours)  
 2    1    Avg Wkly Hrs of Prod or Nonsup Workers on Priv. Nonfarm Payrolls: Goods-Producing  
 2    8    Avg Wkly Hrs of Prod or Nonsup Workers on Priv. Nonfarm Payrolls: Manufacturing Overtime Hours  
 2    1    Average Weekly Hours, Manufacturing (hours)  
 2    1    NAPM Employment Index (percent)  

Table 2c. Macroeconomic Dataset - Real Retail

Group (Code)
Transformation Code
Description
3
7
Sales of Retail Stores (M$, chain 2000)

Table 2d. Macroeconomic Dataset - Manufacturing and Trade Sales

Group (Code)
Transformation Code
Description
4
7
Manufacturing and Trade Sales (M$, chain 1996)

Table 2e. Macroeconomic Dataset - Consumption

Group (Code)
Transformation Code
Description
5
7
Real Consumption: a0m224/gmdc (a0m224 is from TCB)

Table 2f. Macroeconomic Dataset - Housing Starts and Sales

Group (Code)Transformation CodeDescription
 6    4    Housing Starts: Nonfarm (1947-58); Total Farm & Nonfarm (1959-) (Thousands of Units, SAAR)  
 6    4    Housing Starts: Northeast (Thousands of Units, SA)  
 6    4    Housing Starts: Midwest (Thousands of Units, SA)  
 6    4    Housing Starts: South (Thousands of Units, SA)  
 6    4    Housing Starts: West (Thousands of Units, SA)  
 6    4    Housing Authorized: Total New Private Housing Units (Thousands of Units, SAAR)  
 6    4    Houses Authorized by Building Permits: Northeast (Thousands of Units, SA)  
 6    4    Houses Authorized by Building Permits: Midwest (Thousands of Units, SA)  
 6    4    Houses Authorized by Building Permits: South (Thousands of Units, SA)  
 6    4    Houses Authorized by Building Permits: West (Thousands of Units, SA)  

Table 2g. Macroeconomic Dataset - Inventories

Group (Code) Transformation Code Description
7 1 NAPM Inventories Index (percent)
7 7 Manufacturing and Trade Inventories (B$, Chain 2000)
7 8 Ratio of Manufacturying and Trade Inventories to Sales ($, Chain 2000)

Table 2h. Macroeconomic Dataset - Orders

Group (Code) Transformation Code Description
8 1 Purchasing Managers' Index (SA)
8 1 NAPM New Orders Index (percent)
8 1 NAPM Vendor Deliveries Index (percent)
8 7 Manufacturers' New Orders, Consumer Goods And Materials (B$, Chain 1982)
8 7 Manufacturers' New Orders, Durable Goods Industries (B$, Chain 2000)
8 7 Manufacturers' New Orders, Nondefense Capital Goods (M$, Chain 1982)
8 7 Manufacturers' Unfilled Orders, Durable Goods Industries (B$, Chain 2000)

Table 2i. Macroeconomic Dataset - Equities

Group (Code) Transformation Code Description
9 7 S&P's Common Stock Price Index: Composite (1941-43=10)
9 7 S&P's Common Stock Price Index: Industrials (1941-43=10)
9 8 S&P's Composite Common Stock: Dividend Yield (percent p.a.)
9 7 S&P's Composite Common Stock: Price-Earnings Ratio (percent, NSA)

Table 2j. Macroeconomic Dataset - Exchange Rates

Group (Code) Transformation Code Description
10 7 United States: Effective Exchange Rate (MERM model)(index number)
10 7 Foreign Exchange Rate: Switzerland (Swiss Franc per US$)
10 7 Foreign Exchange Rate: Japan (Yen per US$)
10 7 Foreign Exchange Rate: United Kingdom (US$ per Sterling)
10 7 Foreign Exchange Rate: Canada (Canadian Dollar per US$)

Table 2k. Macroeconomic Dataset - Interest Rates

Group (Code) Transformation Code Description
11 1 Interest Rate: Effective Federal Funds (percent p.a., NSA)

Table 2l. Macroeconomic Dataset - Money and Credit Quantity Aggregates

Group (Code) Transformation Code Description
12 7 Money Stock: M1 (B$, SA)
12 7 Money Stock: M2 (B$, SA)
12 7 Money Stock: M3 (B$, SA)
12 7 Money Supply - M2 In 1996 Dollars
12 7 Monetary Base, Adj For Reserve Requirement Changes (M$, SA)
12 7 Depository Inst Reserves:Total, Adj For Reserve Req Chgs (M$, SA)
12 7 Depository Inst Reserves:Nonborrowed,Adj Res Req Chgs (M$, SA)
12 7 Commercial & Industrial Loans Oustanding In 1996 Dollars
12 1 Weekly Report of Commercial Bank Lending: Net Change Commercial & Industrial Loans (B$, SAAR)
12 7 Consumer Credit Outstanding - Nonrevolving
12 8 Ratio of Consumer Installment Credit To Personal Income (percent)

Table 2m. Macroeconomic Dataset - Price Indexes

Group (Code) Transformation Code Description
13 7 PPI: Finished Goods (1982=100, SA)
13 7 PPI: Finished Consumer Goods (1982=100, SA)
13 7 PPI: Intermediate Materials, Supplies & Components (1982=100, SA)
13 7 PPI: Crude Materials (1982=100, SA)
13 7 Spot market price index: BLS & CRB: all commodities (1967=100)
13 7 Index of Sensitive Materials Prices (1990=100)
13 1 NAPM Commodity Prices Index (percent)
13 7 CPI-U: All Items (1982-84=100, SA)
13 7 CPI-U: Apparel & Upkeep (1982-84=100, SA)
13 7 CPI-U: Transportation (1982-84=100, SA)
13 7 CPI-U: Medical Care (1982-84=100, SA)
13 7 CPI-U: Commodities (1982-84=100, SA)
13 7 CPI-U: Durables (1982-84=100, SA)
13 7 CPI-U: Services (1982-84=100, SA)
13 7 CPI-U: All Items Less Food (1982-84=100, SA)
13 7 CPI-U: All Items Less Shelter (1982-84=100, SA)
13 7 CPI-U: All Items Less Midical Care (1982-84=100, SA)
13 7 PCE, Implicit Price Deflator: PCE (1987=100)
13 7 PCE, Implicit Price Deflator: PCE; Durables (1987=100)
13 7 PCE, Implicit Price Deflator: PCE; Nondurables (1996=100)
13 7 PCE, Implicit Price Deflator: PCE; Services (1987=100)

Table 2n. Macroeconomic Dataset - Average Hourly Earnings

Group (Code) Transformation Code Description
14 7 Avg Hourly Earnings of Prod or Nonsup Workers On Priv. Nonfarm Payrolls - Goods-Producing
14 7 Avg Hourly Earnings of Prod or Nonsup Workers On Priv. Nonfarm Payrolls - Construction
14 7 Avg Hourly Earnings of Prod or Nonsup Workers On Priv. Nonfarm Payrolls - Manufacturing

Table 2o. Macroeconomic Dataset - Miscellaneous

Group (Code) Transformation Code Description
15 8 University of Michigan Index of Consumer Expectations

Notes: The table lists the individual macro series that we use to construct macro factors. The series are categorized in 15 groups: (1) real output and income, (2) employment and hours, (3) real retail, (4) manufacturing and trade sales, (5) consumption, (6) housing starts and sales, (7) inventories, (8) orders, (9) stock prices, (10) exchange rates, (11) federal funds rate, (12) money and credit quantity aggregates, (13) prices indices, (14) average hourly earnings and (15) miscellaneous. The transformations applied to original series are coded as: 1 ≡ no transformation (levels are used), 4 ≡ logarithm of the level, 7 ≡ annual first differences of the log levels and 8 ≡ annual first differences of the levels. The sample period is January 1970 - December 2003 (408 observations). Series are from the Global Insights Basic Economics Database and The Conference Board’s Indicators Database. "[N]SA" stands from (Non-)Seasonally Adjusted whereas "SAAR" stands for Seasonally Adjusted Annual Rate.

Table 3a. [T] RMSPE 1994:1 - 2003:12, 1-Month Forecast Horizon - Models

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
RW 101.59 30.12
[0.00]
21.18**
[0.93]
21.82
[0.11]
25.71**
[0.84]
29.12*
[0.93]
30.48**
[1.00]
29.30**
[1.00]
27.95**
[1.00]

Table 3b. [T] RMSPE 1994:1 - 2003:12, 1-Month Forecast Horizon - Panel A: Models Without Macro Factors

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
RW 1.02 1.04
[0.00]
1.07*
[0.77]
1.06
[0.00]
1.05*
[0.30]
1.03
[0.43]
1.01**
[0.69]
1.01**
[0.79]
1.01**
[0.48]
VAR 1.06 0.83**
[1.00]
1.03*
[0.19]
1.23
[0.00]
1.14
[0.00]
1.13
[0.00]
1.04**
[0.04]
1.05
[0.03]
1.11
[0.25]
NS2-AR 1.10 0.94
[0.00]
1.13*
[0.00]
1.27
[0.00]
1.24
[0.00]
1.19
[0.00]
1.11*
[0.00]
1.06
[0.00]
1.07**
[0.03]
NS2-VAR 1.04 0.94
[0.00]
0.96**
[0.90]
1.10
[0.00]
1.10
[0.00]
1.11
[0.00]
1.06**
[0.00]
1.03*
[0.48]
1.06*
[0.02]
NS1 1.06 1.16
[0.00]
1.09
[0.07]
1.08
[0.00]
1.05**
[0.13]
1.10
[0.00]
1.07**
[0.15]
1.04
[0.80]
1.06*
[0.35]
ATSM 1.07 0.84**
[0.99]
0.93**
[0.84]
1.15
[0.00]
1.23
[0.00]
1.18
[0.00]
1.04**
[0.69]
1.08
[0.00]
1.07*
[0.38]

Table 3c. [T] RMSPE 1994:1 - 2003:12, 1-Month Forecast Horizon - Panel B: Models With Macro Factors

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
AR-X 0.99 0.98
[0.00]
0.95**
[1.00]
0.96**
[1.00]
0.98**
[1.00]
0.98**
[1.00]
0.99**
[1.00]
1.00**
[1.00]
0.99**
[1.00]
VAR-X 1.02 0.83**
[1.00]
0.99**
[0.85]
1.03
[0.00]
1.01**
[0.68]
1.12
[0.00]
1.02**
[0.56]
1.02**
[0.79]
1.03**
[0.08]
NS2-AR-X 1.09 0.90
[0.08]
1.22
[0.00]
1.31
[0.00]
1.28
[0.00]
1.17
[0.00]
1.05**
[0.46]
1.06
[0.34]
1.06**
[0.03]
NS2-VAR-X 1.05 0.83**
[1.00]
1.05**
[0.72]
1.17
[0.00]
1.20
[0.00]
1.13
[0.00]
1.03**
[0.51]
1.05
[0.39]
1.05**
[0.03]
NS1-X 1.05 0.98
[0.00]
1.01**
[0.86]
1.04
[0.00]
1.08
[0.00]
1.10
[0.00]
1.04**
[0.34]
1.05
[0.58]
1.06**
[0.03]
ATSM-X 1.13 0.85**
[1.00]
1.13*
[0.87]
1.18
[0.00]
1.29
[0.00]
1.42
[0.00]
1.04**
[0.19]
0.99**
[0.06]
1.06**
[0.00]

Table 3d. [T] RMSPE 1994:1 - 2003:12, 1-Month Forecast Horizon - Panel C: Forecast Combinations

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
FC-EW 1.02 0.91 0.98 1.08 1.08 1.09 1.02 1.02 1.03
FC-MSPE 1.02 0.89 0.98 1.07 1.06 1.08 1.02 1.02 1.03
FC-EW-X 1.01 0.85 0.97 1.03 1.06 1.09 1.00 1.01 1.01
FC-MSPE-X 1.00 0.85 0.96 1.01 1.04 1.07 1.00 1.01 1.01
FC-EW-ALL 1.00 0.86 0.94 1.02 1.05 1.08 1.01 1.01 1.02
FC-MSPE-ALL 1.00 0.85 0.94 1.01 1.04 1.07 1.01 1.01 1.02
FC-MCS-EW 0.99 0.82 0.94 0.97 0.98 0.99 1.01 1.01 1.01
FC-MCS-MSPE 0.99 0.82 0.94 0.97 0.98 0.99 1.01 1.01 1.01

Notes: The table reports the [Trace] Root Mean Squared Prediction Error ([T]RMPSE) for individual yield models, without and with macro factors in Panels A and B, respectively. Panel C shows results for different forecast combination methods. All results are for a 1-month forecast horizon for the out-of-sample period 1994:1 - 2003:12 (R = 120 forecasts). The first line in the table reports the value of [T]RMSPE (expressed in basis points) for the Random Walk model (RW), while all other lines reports statistics relative to the RW. Numbers smaller than one (shown in bold) indicate that models outperform the random walk, whereas numbers larger than one indicate underperformance. Two stars indicate that a model belongs to the model set $\displaystyle \widehat{M}_{0.25}^{\ast} $ whereas models with one star belong to $\displaystyle \widehat{M}_{0.10}^{\ast} $. The following model abbreviations are used in the table: RW stands for the Random Walk, (V)AR for the first-order (Vector) Autoregressive Model, NS2-(V)AR for the two-step Nelson-Siegel model with a (V)AR specification for the factors, NS1 for the one-step Nelson-Siegel model, ATSM for the affine model. The affix “X” indicates that macro factors have been incorporated in a model as additional explanatory variables. FC-EW and FC-MSPE stand for forecast combinations based on equal weights and MSPE-based weights, respectively, and FC-MCS for forecasting combinations using the pre-filtered model set $\displaystyle \widehat{M}_{0.25}^{\ast} $. For the forecast combinations “-X” indicates that forecasts are combined only from models with macro factors whereas “-ALL” indicates that forecasts from all models, both macro as well as yield-only, are combined. No affix in the first two rows of Panel C means that yields-only models are combined. The numbers between parentheses in Panels A and B include the fraction of times a model is included in $\displaystyle \widehat{M}_{0.25}^{\ast} $ for the expanding forecast sample 1994:1 - 2003:12 in the FC-MCS-EW and FC-MCS-MSPE schemes. The $\displaystyle \widehat{M}_{0.25}^{\ast} $ for these forecast combination schemes are determined using an expanding window, with the initial window being 1989:1 - 1993:12.

Table 4a. [T] RMSPE 1994:1 - 2003:12, 3-Month Forecast Horizon - Models

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
RW 195.81 53.61
[0.00]
48.24**
[0.56]
50.71*
[0.05]
55.36*
[0.14]
59.86*
[0.70]
57.25**
[1.00]
53.47**
[1.00]
49.72**
[1.00]

Table 4b. [T] RMSPE 1994:1 - 2003:12, 3-Month Forecast Horizon - Panel A: Models Without Macro Factors

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
RW 1.05 1.11
[0.00]
1.10*
[0.00]
1.09*
[0.00]
1.08*
[0.06]
1.04*
[0.61]
1.02**
[0.88]
1.03**
[0.86]
1.03**
[0.98]
VAR 1.10 0.90**
[0.41]
1.08*
[0.00]
1.21
[0.00]
1.20
[0.00]
1.16
[0.02]
1.09**
[0.10]
1.08*
[0.44]
1.13**
[0.80]
NS2-AR 1.13 1.02*
[0.00]
1.16*
[0.00]
1.24*
[0.00]
1.26
[0.00]
1.23
[0.00]
1.13**
[0.03]
1.07**
[0.34]
1.06**
[0.75]
NS2-VAR 1.05 0.94*
[0.11]
0.99**
[0.37]
1.08*
[0.00]
1.11
[0.00]
1.11*
[0.00]
1.06**
[0.01]
1.03**
[0.64]
1.05**
[0.81]
NS1 1.06 1.09
[0.00]
1.09
[0.00]
1.11*
[0.00]
1.10*
[0.00]
1.10*
[0.20]
1.06**
[0.56]
1.02**
[0.81]
1.03**
[0.96]
ATSM 1.06 0.85**
[0.68]
0.96**
[0.42]
1.11*
[0.00]
1.18
[0.00]
1.14
[0.00]
1.02**
[0.84]
1.07**
[0.00]
1.06**
[0.91]

Table 4c. [T] RMSPE 1994:1 - 2003:12, 3-Month Forecast Horizon - Panel B: Models With Macro Factors

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
AR-X 0.98 0.98
[0.69]
0.95**
[1.00]
0.96**
[1.00]
0.98**
[1.00]
0.98**
[1.00]
0.99**
[1.00]
0.99**
[1.00]
0.99**
[1.00]
VAR-X 0.99 0.87**
[0.77]
0.98**
[0.62]
1.00*
[0.00]
1.00*
[0.14]
1.03*
[0.70]
0.99**
[1.00]
0.99**
[1.00]
1.00**
[1.00]
NS2-AR-X 1.13 1.03
[0.00]
1.24
[0.00]
1.27
[0.00]
1.28
[0.00]
1.20
[0.00]
1.08**
[0.57]
1.07**
[0.55]
1.04**
[0.80]
NS2-VAR-X 1.07 0.85**
[0.37]
1.04*
[0.00]
1.13*
[0.00]
1.19
[0.00]
1.16
[0.00]
1.05**
[0.42]
1.05**
[0.76]
1.03**
[0.92]
NS1-X 1.03 0.84**
[0.56]
0.96**
[0.62]
1.04*
[0.00]
1.10
[0.00]
1.10
[0.02]
1.04**
[0.71]
1.03**
[0.85]
1.03**
[1.00]
ATSM-X 1.04 0.80**
[1.00]
0.94**
[0.74]
1.04*
[0.00]
1.14
[0.00]
1.20
[0.04]
1.03**
[0.73]
1.00**
[0.86]
1.01**
[0.86]

Table 4d. [T] RMSPE 1994:1 - 2003:12, 3-Month Forecast Horizon - Panel C: Forecast Combinations

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
FC-EW 1.04 0.94 1.02 1.09 1.10 1.09 1.03 1.02 1.03
FC-MSPE 1.04 0.94 1.02 1.09 1.10 1.09 1.04 1.03 1.04
FC-EW-X 1.00 0.87 0.96 1.01 1.05 1.06 1.00 1.00 0.99
FC-MSPE-X 1.00 0.87 0.95 1.01 1.04 1.05 1.01 1.00 1.00
FC-EW-ALL 1.00 0.86 0.93 1.01 1.05 1.06 1.01 1.00 1.00
FC-MSPE-ALL 1.00 0.86 0.94 1.01 1.05 1.06 1.01 1.01 1.01
FC-MCS-EW 1.00 0.83 0.96 0.97 1.00 1.02 1.01 1.02 1.02
FC-MCS-MSPE 1.00 0.83 0.96 0.97 1.00 1.01 1.01 1.02 1.02

Notes: The table reports forecast results for a 3-month horizon for the out-of-sample period 1994:1 - 2003:12. See Table 3 for further details.

Table 5a. [T] RMSPE 1994:1 - 2003:12, 6-Month Forecast Horizon - Models

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
RW 300.94 83.60*
[0.00]
82.31**
[0.34]
85.20**
[0.24]
89.24**
[0.04]
92.74**
[0.90]
86.36**
[0.97]
79.23**
[0.98]
72.50**
[1.00]

Table 5b. [T] RMSPE 1994:1 - 2003:12, 6-Month Forecast Horizon - Panel A: Models Without Macro Factors

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
RW 1.07 1.15
[0.00]
1.12**
[0.00]
1.10**
[0.09]
1.10**
[0.02]
1.06**
[0.67]
1.03**
[0.92]
1.04**
[0.86]
1.04**
[0.90]
VAR 1.20 1.11*
[0.00]
1.22*
[0.00]
1.31*
[0.00]
1.31*
[0.00]
1.24*
[0.00]
1.14**
[0.41]
1.15**
[0.49]
1.21**
[0.73]
NS2-AR 1.12 1.05**
[0.00]
1.12**
[0.00]
1.18**
[0.00]
1.22*
[0.00]
1.20*
[0.00]
1.11**
[0.40]
1.06**
[0.47]
1.06**
[0.76]
NS2-VAR 1.05 1.02*
[0.00]
1.03**
[0.12]
1.09**
[0.09]
1.11*
[0.00]
1.10**
[0.04]
1.04**
[0.55]
1.02**
[0.93]
1.06**
[0.90]
NS1 1.06 1.16
[0.00]
1.12**
[0.00]
1.13**
[0.00]
1.11*
[0.00]
1.08**
[0.15]
1.02**
[0.70]
1.00**
[0.85]
1.03**
[0.80]
ATSM 1.06 0.95**
[0.47]
1.02**
[0.21]
1.12**
[0.01]
1.17*
[0.00]
1.12*
[0.01]
1.01**
[0.96]
1.07**
[0.39]
1.07**
[0.97]

Table 5c. [T] RMSPE 1994:1 - 2003:12, 6-Month Forecast Horizon - Panel B: Models With Macro Factors

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
AR-X 1.00 0.97**
[1.00]
0.96**
[1.00]
0.97**
[1.00]
0.99**
[1.00]
1.00**
[1.00]
1.01**
[1.00]
1.00**
[1.00]
1.01**
[1.00]
VAR-X 0.98 0.93**
[0.90]
0.98**
[0.51]
1.00**
[0.22]
1.01**
[0.45]
1.00**
[0.90]
0.97**
[0.97]
0.97**
[0.98]
0.99**
[1.00]
NS2-AR-X 1.13 1.10*
[0.00]
1.22*
[0.00]
1.24*
[0.00]
1.26*
[0.00]
1.18*
[0.07]
1.06**
[0.70]
1.05**
[0.71]
1.04**
[0.84]
NS2-VAR-X 1.07 0.94**
[0.49]
1.07**
[0.23]
1.14**
[0.24]
1.19*
[0.00]
1.15*
[0.07]
1.04**
[0.84]
1.03**
[0.95]
1.03**
[0.96]
NS1-X 1.02 0.87**
[0.88]
0.96**
[0.50]
1.03**
[0.21]
1.09*
[0.00]
1.08**
[0.19]
1.01**
[0.86]
1.00**
[0.90]
1.01**
[0.93]
ATSM-X 1.02 0.84**
[1.00]
0.95**
[0.61]
1.04**
[0.24]
1.11*
[0.00]
1.12**
[0.32]
0.99**
[0.97]
0.98**
[0.85]
1.01**
[0.88]

Table 5d. [T] RMSPE 1994:1 - 2003:12, 6-Month Forecast Horizon - Panel C: Forecast Combinations

Models [T]RMSPE 1m 3m 6m 1y 2y 5y 7y 10y
FC-EW 1.05 1.02 1.05 1.10 1.11 1.08 1.02 1.02 1.04
FC-MSPE 1.05 1.03 1.07 1.10 1.11 1.08 1.02 1.01 1.03
FC-EW-X 0.99 0.90 0.96 1.01 1.04 1.04 0.99 0.98 0.99
FC-MSPE-X 0.97 0.90 0.96 0.99 1.01 1.01 0.96 0.95 0.95
FC-EW-ALL 0.99 0.90 0.95 1.00 1.04 1.03 0.98 0.98 0.99
FC-MSPE-ALL 0.98 0.91 0.96 1.01 1.04 1.02 0.97 0.96 0.97
FC-MCS-EW 0.98 0.92 0.98 0.99 0.98 1.00 0.99 0.99 0.99
FC-MCS-MSPE 0.98 0.91 0.98 0.99 0.98 1.00 0.99 0.99 0.99

Notes: The table reports forecast results for a 6-month horizon for the out-of-sample period 1994:1 - 2003:12. See Table 3 for further details.

Table 6a. [T] RMSPE 1994:1 - 2003:12, 12-Month Forecast Horizon - Models

Models[T]RMSPE1m3m6m1y2y5y7y10y
RW452.51136.94**
[0.12]
140.61**
[0.79]
145.03**
[0.94]
146.89**
[0.69]
141.77**
[0.96]
121.21**
[0.95]
108.58**
[0.95]
98.96**
[0.85]

Table 6b. [T] RMSPE 1994:1 - 2003:12, 12-Month Forecast Horizon - Panel A: Models Without Macro Factors

Models[T]RMSPE1m3m6m1y2y5y7y10y
RW1.101.15**
[0.01]
1.11**
[0.48]
1.09**
[0.71]
1.10**
[0.48]
1.09**
[0.85]
1.07**
[0.89]
1.09**
[0.48]
1.10**
[0.46]
VAR1.431.36
[0.00]
1.41*
[0.00]
1.44*
[0.01]
1.42*
[0.02]
1.40*
[0.21]
1.41*
[0.28]
1.46
[0.23]
1.55
[0.18]
NS2-AR1.101.02**
[0.00]
1.04**
[0.35]
1.06**
[0.45]
1.10**
[0.29]
1.14**
[0.36]
1.13**
[0.57]
1.12**
[0.47]
1.13**
[0.68]
NS2-VAR1.081.09**
[0.03]
1.07**
[0.65]
1.08**
[0.70]
1.08**
[0.59]
1.09**
[0.64]
1.07**
[0.77]
1.07**
[0.93]
1.12**
[0.81]
NS11.091.21*
[0.00]
1.15**
[0.00]
1.13**
[0.15]
1.10**
[0.28]
1.09**
[0.48]
1.05**
[0.77]
1.04**
[0.91]
1.08**
[0.81]
ATSM1.101.06**
[0.15]
1.07**
[0.72]
1.11**
[0.35]
1.14**
[0.22]
1.12**
[0.50]
1.04**
[0.93]
1.12**
[0.63]
1.13**
[0.95]

Table 6c. [T] RMSPE 1994:1 - 2003:12, 12-Month Forecast Horizon - Panel B: Models With Macro Factors

Models[T]RMSPE1m3m6m1y2y5y7y10y
AR-X1.020.95**
[1.00]
0.95*
[1.00]
0.98**
[1.00]
1.00**
[1.00]
1.03**
[1.00]
1.06**
[1.00]
1.05**
[1.00]
1.06**
[0.92]
VAR-X0.980.97**
[0.67]
0.97**
[0.92]
0.98**
[0.95]
0.99**
[0.96]
0.99**
[0.96]
0.96**
[0.94]
0.97**
[0.95]
0.99**
[0.95]
NS2-AR-X1.141.15**
[0.19]
1.19**
[0.50]
1.18**
[0.55]
1.19**
[0.46]
1.16**
[0.46]
1.09**
[0.86]
1.09**
[0.72]
1.08**
[0.76]
NS2-VAR-X1.111.07**
[0.60]
1.13**
[0.80]
1.14**
[0.79]
1.17**
[0.58]
1.15**
[0.63]
1.07**
[0.94]
1.06**
[0.95]
1.05**
[0.85]
NS1-X1.010.91**
[0.60]
0.96**
[0.80]
1.00**
[0.76]
1.05**
[0.52]
1.06**
[0.73]
1.01**
[0.90]
1.00**
[0.93]
1.01**
[0.83]
ATSM-X 1.020.93**
[0.82]
0.99**
[0.88]
1.04**
[0.74]
1.07**
[0.53]
1.08**
[0.81]
0.99**
[0.94]
1.00**
[0.94]
1.02**
[0.86]

Table 6d. [T] RMSPE 1994:1 - 2003:12, 12-Month Forecast Horizon - Panel C: Forecast Combinations

Models[T]RMSPE1m3m6m1y2y5y7y10y
FC-EW1.081.081.081.091.101.091.071.081.11
FC-MSPE1.091.111.101.111.111.101.071.081.10
FC-EW-X1.000.940.970.991.021.031.001.001.00
FC-MSPE-X0.950.950.970.970.980.970.940.940.92
FC-EW-ALL0.990.930.950.971.001.010.991.001.01
FC-MSPE-ALL0.980.960.980.991.001.000.970.970.97
FC-MCS-EW1.000.991.021.031.031.020.970.990.99
FC-MCS-MSPE1.000.991.021.031.021.010.970.980.99

Notes: The table reports forecast results for a 12-month horizon for the out-of-sample period 1994:1 - 2003:12. See Table 3 for further details.

Figure 1a. U.S. Zero-Coupon Yields: Full Sample 1970:1 - 2003:12

Data for Figure 1a immediately follows.

Data for Figure 1a

Month3m Yield1y Yield2y Yield5y Yield10y Yield
Jan-708.0198.0107.9898.0677.515
Feb-706.9836.9227.0247.1457.020
Mar-706.4956.6116.9117.0527.163
Apr-707.0527.4927.5817.7427.812
May-707.0797.4417.7457.6067.628
Jun-706.5857.1927.4537.5437.746
Jul-706.4666.8117.1867.3737.466
Aug-706.3966.8007.0127.2557.512
Sep-705.9236.5946.5557.0507.266
Oct-705.9386.3246.5116.8777.096
Nov-705.0905.0995.3135.9066.308
Dec-704.9154.8865.4035.9226.142
Jan-714.1944.3104.6435.6556.068
Feb-713.4373.7724.2785.3045.786
Mar-713.6293.7584.1474.9775.313
Apr-713.9614.5525.2165.9736.055
May-714.3784.8865.4066.2066.243
Jun-715.2716.0576.2676.7836.792
Jul-715.3696.1096.3156.8916.889
Aug-714.4775.2705.4476.0246.279
Sep-714.6535.2715.3995.9655.902
Oct-714.3524.5894.9565.6605.800
Nov-714.3774.7435.0595.7226.182
Dec-713.7144.1814.8285.4265.869
Jan-723.3824.1204.8045.7186.088
Feb-723.4704.2914.7695.6656.283
Mar-723.8744.9375.5285.9996.269
Apr-723.6484.5275.1095.7986.240
May-723.8354.6314.9475.7156.249
Jun-724.1015.2545.4385.9096.301
Jul-723.8574.9505.2485.8916.329
Aug-724.6075.4865.6356.0836.410
Sep-724.6415.6875.7916.0556.497
Oct-724.8205.5415.7586.0946.417
Nov-724.9515.3965.6446.0096.333
Dec-725.2185.6345.9156.1706.400
Jan-735.7706.1486.2136.3036.451
Feb-735.9436.4096.5226.5946.551
Mar-736.5076.9956.8046.6516.581
Apr-736.3856.7056.6366.5736.551
May-737.0526.9496.7346.5996.825
Jun-737.6297.7826.9666.7206.795
Jul-738.4628.6327.9667.6447.199
Aug-738.8248.3707.7137.0547.032
Sep-737.1107.6856.9566.5446.719
Oct-737.4847.1266.7266.6366.578
Nov-737.4757.4176.6996.6126.577
Dec-737.5967.1296.6936.6866.738
Jan-747.6316.8906.6746.7466.895
Feb-747.6007.0256.8186.8106.744
Mar-748.4818.1287.6907.4197.202
Apr-749.0808.6768.1547.9427.705
May-748.2418.4727.9787.7347.684
Jun-747.7498.6178.2668.0807.313
Jul-747.8118.6638.3728.1927.598
Aug-749.1129.6748.6598.3817.830
Sep-746.3607.8978.0377.8447.593
Oct-747.9517.6477.7087.7797.383
Nov-747.6087.5087.1977.3937.279
Dec-747.1536.8807.1737.0976.896
Jan-755.7676.0916.6447.1626.938
Feb-755.4855.8686.1176.9406.892
Mar-755.6526.1906.6897.2977.595
Apr-755.5736.6657.3877.8557.836
May-755.2735.9966.7747.4157.790
Jun-756.0286.7037.0667.5957.285
Jul-756.3517.1737.5427.8377.313
Aug-756.4747.3257.6227.9807.923
Sep-756.6427.5458.0078.1157.954
Oct-755.5996.1616.9137.5447.865
Nov-755.6396.4397.1387.7107.786
Dec-755.2855.9776.6197.3577.772
Jan-764.8025.5166.2557.3847.771
Feb-765.0935.9956.6687.3367.752
Mar-765.0475.9976.6207.2947.164
Apr-764.9955.9286.5697.2697.293
May-765.5956.5867.1517.6237.897
Jun-765.4616.3466.9217.4677.812
Jul-765.2736.0236.6577.2717.574
Aug-765.1715.8266.4827.1677.630
Sep-765.1575.7266.2276.9127.547
Oct-764.9845.4205.9186.7317.448
Nov-764.4994.9185.3296.0567.163
Dec-764.4134.7715.3056.0916.892
Jan-774.8275.5916.0306.7567.401
Feb-774.7895.4625.9926.8847.377
Mar-774.6125.3225.9206.8467.340
Apr-774.7665.4626.0016.8347.466
May-775.1045.6496.0856.8056.984
Jun-775.0745.6135.9766.6206.880
Jul-775.4996.1146.3716.9117.375
Aug-775.6666.2416.4856.8457.274
Sep-776.0226.4796.7016.9987.354
Oct-776.2066.7877.0247.2797.467
Nov-776.1906.6306.9887.2047.470
Dec-776.2546.8407.0907.4537.705
Jan-786.5517.0757.3317.5947.845
Feb-786.5357.1387.4247.7307.932
Mar-786.6167.3217.5537.8128.037
Apr-786.3827.3417.7137.9108.107
May-786.7807.7687.9428.1278.300
Jun-787.1838.1978.2938.3178.477
Jul-786.9718.0568.2818.2518.414
Aug-787.7038.2598.2688.1938.198
Sep-788.1848.5528.4468.2818.374
Oct-788.8969.5119.2378.7258.684
Nov-789.2269.7509.2928.5398.633
Dec-789.50010.1639.6419.0208.867
Jan-799.5219.7889.3758.7068.694
Feb-799.6849.9149.6139.0418.856
Mar-799.6789.6079.4418.9218.813
Apr-799.7619.9899.6349.0619.006
May-799.8199.6279.2898.6858.850
Jun-799.1679.1328.6738.3488.624
Jul-799.3899.4299.0538.5918.773
Aug-7910.06110.0559.5488.8578.915
Sep-7910.39510.5759.7809.0949.128
Oct-7912.44912.43111.64610.62210.307
Nov-7911.64011.17810.9629.97310.056
Dec-7912.31411.17710.8469.96310.011
Jan-8012.34311.97911.36510.59810.754
Feb-8014.40014.83314.15512.19111.558
Mar-8015.41615.14513.98512.24511.911
Apr-8010.63810.38210.52110.17910.553
May-807.9218.5228.7699.59110.256
Jun-808.0678.2208.7489.40210.000
Jul-808.8118.9109.48010.08310.665
Aug-8010.19311.00110.98511.28611.246
Sep-8011.61411.75911.71311.51011.516
Oct-8013.08112.95312.63412.25911.993
Nov-8014.66714.14813.15112.57912.287
Dec-8014.72413.38712.38311.88111.631
Jan-8115.03613.49012.68312.26711.978
Feb-8114.65714.03413.18313.02112.647
Mar-8112.80912.61212.62912.86312.404
Apr-8115.32514.52114.29513.74613.193
May-8115.54814.42013.76313.11912.837
Jun-8114.68313.91513.99713.23713.189
Jul-8115.35015.34915.14914.02114.039
Aug-8116.02015.82215.65014.76914.702
Sep-8114.89815.44415.60315.00514.925
Oct-8113.11313.80514.02114.27714.016
Nov-8110.60211.46011.57812.62312.678
Dec-8111.36012.90813.21113.44713.582
Jan-8212.83513.56313.68613.62013.584
Feb-8212.74413.75413.83413.45613.660
Mar-8213.57613.66613.83213.55313.441
Apr-8212.64013.37013.48313.13813.416
May-8211.81212.66913.03913.16713.263
Jun-8213.11013.97214.07414.03213.714
Jul-8210.45612.28812.72613.19713.098
Aug-828.54611.23911.63312.39612.248
Sep-827.78610.21010.96511.41910.975
Oct-828.0709.3509.91110.35610.662
Nov-828.4399.1419.71710.46310.124
Dec-828.0918.5089.27710.2749.833
Jan-838.2718.7189.36410.47610.385
Feb-838.1078.4569.14610.0489.889
Mar-838.8429.1269.67710.39710.175
Apr-838.2608.6069.11510.0299.835
May-838.8559.2349.79510.56210.517
Jun-838.9889.40510.04410.75610.610
Jul-839.46110.20010.68611.52911.478
Aug-839.48310.29810.85111.74811.512
Sep-838.9109.66010.27911.28310.994
Oct-838.6959.51210.33011.23711.384
Nov-839.0929.68710.40111.11911.327
Dec-839.1889.80310.52211.36611.469
Jan-849.1129.54610.34311.16811.340
Feb-849.3689.92510.74511.50311.698
Mar-849.97910.65811.26212.02812.187
Apr-849.96010.71311.59112.29712.452
May-8410.00611.90112.64213.41013.595
Jun-8410.20011.92812.77713.35713.439
Jul-8410.66311.56312.23612.53812.484
Aug-8410.90511.60812.20112.47212.388
Sep-8410.43711.05611.72412.17212.023
Oct-849.2299.98910.83311.27911.316
Nov-848.6499.48510.25311.04711.272
Dec-847.9759.0249.79310.97811.263
Jan-858.2418.8449.68910.5910.878
Feb-858.7089.68310.41311.31311.663
Mar-858.379.49210.16411.11711.426
Apr-857.9998.9299.77210.77811.228
May-857.298.078.7489.73310.204
Jun-856.9927.6698.5369.71710.193
Jul-857.4348.1588.8429.92610.503
Aug-857.37.8838.7579.71410.166
Sep-857.2217.8258.7179.810.27
Oct-857.3527.7768.5439.50710.007
Nov-857.3217.6978.2729.1859.598
Dec-857.1747.4847.8578.6299.015
Jan-867.1247.6017.8348.659.135
Feb-867.1717.3937.5588.0357.977
Mar-866.4746.7966.8347.3817.248
Apr-866.2246.5016.7067.4047.25
May-866.436.8467.1988.1037.86
Jun-866.0956.4236.7787.5187.584
Jul-865.9086.2016.4647.3947.692
Aug-865.2595.4435.8296.6426.919
Sep-865.3265.736.3297.2857.695
Oct-865.3045.6646.1547.0577.369
Nov-865.4965.7326.0896.7477.082
Dec-865.786.0656.36.9187.18
Jan-875.715.9186.1886.757.16
Feb-875.5595.9496.2256.7447.194
Mar-875.6816.1756.4577.0617.515
Apr-875.636.8417.2457.8438.155
May-875.8137.0377.5318.1188.392
Jun-875.8216.8177.3548.0128.303
Jul-876.1826.9497.4828.1388.618
Aug-876.367.2117.8278.4268.934
Sep-876.7547.8838.4489.1019.527
Oct-875.396.6677.4428.3768.797
Nov-875.4516.8767.5678.4638.923
Dec-875.7947.2477.6458.3088.761
Jan-885.7596.6727.0747.6868.239
Feb-885.7456.6127.0097.5558.129
Mar-885.8256.8547.2837.9788.539
Apr-886.117.1037.5648.2518.848
May-886.6427.678.0588.6569.134
Jun-886.7017.5147.8718.3158.751
Jul-887.0977.8958.28.5979.041
Aug-887.4918.1128.5398.7969.136
Sep-887.4127.9928.2768.4988.754
Oct-887.5347.9078.0828.2178.549
Nov-888.0058.4698.6478.7358.894
Dec-888.3018.9128.919.0058.891
Jan-898.5778.8898.9128.8358.773
Feb-898.9179.369.3179.1629.052
Mar-899.1319.6419.5249.2938.993
Apr-898.6219.0428.9748.8998.78
May-898.8188.7718.6118.5478.357
Jun-898.1718.1297.9097.9447.908
Jul-897.9097.5037.3677.4437.727
Aug-898.0818.1188.2438.1348.051
Sep-898.0928.3218.2698.2288.094
Oct-897.9527.7517.6817.7627.761
Nov-897.7657.6747.5887.6867.678
Dec-897.7267.7477.7427.7647.783
Jan-907.9228.0818.1038.258.279
Feb-907.9548.0558.2468.3788.321
Mar-907.998.3098.4428.5358.455
Apr-908.0468.5438.7588.8878.847
May-907.9318.1268.3118.4878.404
Jun-907.9197.8958.0368.2748.271
Jul-907.6677.5767.7498.048.291
Aug-907.5587.6347.9038.4588.767
Sep-907.2987.5647.8428.3928.747
Oct-907.2697.467.6078.1658.619
Nov-907.1737.3577.3757.8698.179
Dec-906.6086.9237.0587.6628.06
Jan-916.326.6136.9237.5288.091
Feb-916.1656.5016.917.578.033
Mar-915.8566.3136.9167.6298.053
Apr-915.6176.1776.6847.5578.077
May-915.6426.0566.7717.6218.085
Jun-915.656.1986.7887.828.262
Jul-915.6396.0756.6957.7128.214
Aug-915.4345.6356.247.2777.898
Sep-915.2085.3665.9296.8687.593
Oct-914.915.1575.6156.7127.733
Nov-914.4294.765.2936.4587.644
Dec-913.9144.1654.7325.9237.089
Jan-923.9064.3545.0466.4347.64
Feb-923.9994.4135.1976.567.533
Mar-924.1034.6125.5676.927.713
Apr-923.7614.3795.4066.9227.82
May-923.764.1875.1226.6277.415
Jun-923.6234.0054.8036.3137.3
Jul-923.2313.5914.3735.8476.921
Aug-923.2093.4384.1125.6156.768
Sep-922.7323.1073.7775.3596.659
Oct-923.0073.6234.3425.9047.067
Nov-923.3453.9254.7426.2337.209
Dec-923.1273.6534.5056.0556.975
Jan-932.9493.4354.155.5936.685
Feb-932.9973.3083.8755.2266.244
Mar-932.9293.3553.9185.2516.319
Apr-932.9523.2223.7895.1566.36
May-933.1113.5774.1795.3746.431
Jun-933.0793.4163.9865.0566.03
Jul-933.083.5054.0845.1546.022
Aug-933.0523.3563.8354.7985.644
Sep-932.9633.3763.8524.785.617
Oct-933.0823.4533.9384.8185.641
Nov-933.1883.6344.1745.1486.04
Dec-933.0653.6444.2075.2136.04
Jan-943.0163.5194.0795.0185.85
Feb-943.4314.0654.6395.5876.201
Mar-943.5364.485.176.2066.873
Apr-943.9455.0035.686.5927.148
May-944.275.3015.9286.7237.234
Jun-944.2235.4316.0876.9217.454
Jul-944.3535.2995.9076.6727.281
Aug-944.6445.4696.0866.7547.263
Sep-944.7765.8876.4977.2187.678
Oct-945.1386.0486.7327.4127.855
Nov-945.6656.8417.2637.6737.856
Dec-945.6627.1537.5037.6747.742
Jan-955.9326.7487.1267.4197.56
Feb-955.8686.3456.6686.9617.133
Mar-955.8236.3566.6726.9737.199
Apr-955.8096.26.4696.7677.104
May-955.7425.6995.785.9936.329
Jun-955.5515.5635.7085.8946.281
Jul-955.5275.5765.7926.0766.544
Aug-955.3985.6255.7565.9856.318
Sep-955.3535.6335.7255.9126.202
Oct-955.4215.5145.5335.7266.043
Nov-955.4245.3255.2735.4565.718
Dec-955.0595.095.0885.3075.564
Jan-9654.8894.875.195.605
Feb-964.9825.1445.3635.6676.108
Mar-965.0995.4135.6916.0436.323
Apr-965.15.5375.946.326.634
May-965.1385.6816.1616.5626.787
Jun-965.1445.636.0136.3796.674
Jul-965.2795.8726.1176.4936.749
Aug-965.2495.8326.2316.6366.902
Sep-965.0575.6686.0086.3866.678
Oct-965.1165.4425.6686.0076.302
Nov-965.0985.3775.5085.7566.014
Dec-965.125.465.796.1436.387
Jan-975.1255.4935.8396.1826.48
Feb-975.1965.596.0086.3186.488
Mar-975.2865.9156.3356.6746.827
Apr-975.2565.8096.1936.4926.651
May-975.145.7956.1176.4126.593
Jun-975.1945.6125.9916.3086.429
Jul-975.2035.5055.665.8325.962
Aug-975.1855.6565.8746.136.252
Sep-975.025.5675.7125.9116.035
Oct-975.1735.3035.5675.6335.77
Nov-975.2575.4535.7115.7595.808
Dec-975.3075.4155.5785.6325.683
Jan-985.1585.1675.2635.315.491
Feb-985.2745.3335.4695.5125.54
Mar-985.1345.3185.5035.5445.574
Apr-984.9465.3335.5095.5625.602
May-984.9975.3575.4655.4855.461
Jun-985.0125.3415.4045.3855.346
Jul-985.0495.4395.4185.4675.419
Aug-984.8465.0284.8144.8655.047
Sep-984.3024.5724.2774.3474.443
Oct-984.3234.3994.1674.484.668
Nov-984.494.6354.4784.5624.664
Dec-984.4354.584.5194.5914.599
Jan-994.4374.4594.5314.5274.624
Feb-994.6424.8495.0975.2065.253
Mar-994.4534.6544.9385.1695.231
Apr-994.5184.7265.0115.2665.361
May-994.624.9165.3545.645.512
Jun-994.7345.1585.4565.7595.711
Jul-994.7135.2435.5595.9225.831
Aug-994.9065.4385.655.9685.863
Sep-994.8075.3765.555.8795.792
Oct-995.0455.4945.7236.0455.952
Nov-995.2495.7595.9316.1436.141
Dec-995.3275.8986.1486.396.387
Jan-005.6636.1696.5066.666.557
Feb-005.7356.1016.4416.5696.236
Mar-005.8276.3086.396.2536.047
Apr-005.86.4536.5676.4566.039
May-005.5756.276.5976.4536.116
Jun-005.8396.4116.286.1585.904
Jul-006.1946.3676.2046.1345.913
Aug-006.2566.1316.0875.9325.573
Sep-006.1666.2015.8855.7975.703
Oct-006.3086.2095.8245.7065.667
Nov-006.1625.8355.5485.3895.41
Dec-005.8495.4245.0514.9895.097
Jan-014.9664.6554.5674.8475.162
Feb-014.8334.4184.3864.6994.859
Mar-014.2664.1644.1864.624.919
Apr-013.8534.0364.2784.9385.372
May-013.6053.7924.2134.9775.436
Jun-013.6283.8824.2335.0675.477
Jul-013.5213.4583.7744.6715.166
Aug-013.3353.3343.6094.4974.844
Sep-012.3492.5172.8224.0554.682
Oct-012.0271.9572.373.6754.367
Nov-011.7822.0512.844.1034.911
Dec-011.6982.0533.0664.4475.206
Jan-021.7592.2783.1534.5195.205
Feb-021.7572.1973.0444.3584.93
Mar-021.7852.6893.6745.0035.46
Apr-021.7492.253.2164.5845.193
May-021.7222.273.1874.4145.187
Jun-021.6891.942.8754.1494.993
Jul-021.6931.7242.2233.6364.716
Aug-021.6671.7482.1093.2844.234
Sep-021.5431.4311.6812.6733.751
Oct-021.4361.3371.6652.8764.1
Nov-021.2191.5042.0393.3194.305
Dec-021.1871.2091.5822.8093.976
Jan-031.1691.2861.6913.0444.137
Feb-031.2051.2341.512.7263.805
Mar-031.1041.1451.4862.8253.948
Apr-031.1111.151.4772.8874.013
May-031.111.1631.3172.3513.483
Jun-030.8761.041.2992.5013.662
Jul-030.941.2261.7383.3624.59
Aug-030.9881.31.9613.5134.592
Sep-030.9281.0551.4622.884.122
Oct-030.9371.2391.8213.2964.492
Nov-030.9261.4492.0343.3874.458
Dec-030.9281.2281.8393.2644.42

Figure 1b. U.S. Zero-Coupon Yields: Forecast Sample 1994:1 - 2003:12

Data for Figure 1b immediately follows.

Notes: The figure shows time-series plots of our end-of-month U.S. zero coupon yields (for a selected set of maturities). The yields have been constructed using the Fama and Bliss (1987) bootstrap method. The full sample period is January 1970 - December 2003 (408 observations), and is shown in Panel (a). The solid vertical line shows the beginning of the out-of-sample period January 1994 - December 2003 (120 observations). The start of the initial out-of-sample calibrating period for model weights in the forecast combination scheme is indicated by the dotted line. The calibration and out-of-sample periods are shown separately in Panel (b). Yellow bars highlight NBER recession periods.

Data for Figure 1b

Month3m Yield1y Yield2y Yield5y Yield10y Yield
Jan-943.0163.5194.0795.0185.85
Feb-943.4314.0654.6395.5876.201
Mar-943.5364.485.176.2066.873
Apr-943.9455.0035.686.5927.148
May-944.275.3015.9286.7237.234
Jun-944.2235.4316.0876.9217.454
Jul-944.3535.2995.9076.6727.281
Aug-944.6445.4696.0866.7547.263
Sep-944.7765.8876.4977.2187.678
Oct-945.1386.0486.7327.4127.855
Nov-945.6656.8417.2637.6737.856
Dec-945.6627.1537.5037.6747.742
Jan-955.9326.7487.1267.4197.56
Feb-955.8686.3456.6686.9617.133
Mar-955.8236.3566.6726.9737.199
Apr-955.8096.26.4696.7677.104
May-955.7425.6995.785.9936.329
Jun-955.5515.5635.7085.8946.281
Jul-955.5275.5765.7926.0766.544
Aug-955.3985.6255.7565.9856.318
Sep-955.3535.6335.7255.9126.202
Oct-955.4215.5145.5335.7266.043
Nov-955.4245.3255.2735.4565.718
Dec-955.0595.095.0885.3075.564
Jan-9654.8894.875.195.605
Feb-964.9825.1445.3635.6676.108
Mar-965.0995.4135.6916.0436.323
Apr-965.15.5375.946.326.634
May-965.1385.6816.1616.5626.787
Jun-965.1445.636.0136.3796.674
Jul-965.2795.8726.1176.4936.749
Aug-965.2495.8326.2316.6366.902
Sep-965.0575.6686.0086.3866.678
Oct-965.1165.4425.6686.0076.302
Nov-965.0985.3775.5085.7566.014
Dec-965.125.465.796.1436.387
Jan-975.1255.4935.8396.1826.48
Feb-975.1965.596.0086.3186.488
Mar-975.2865.9156.3356.6746.827
Apr-975.2565.8096.1936.4926.651
May-975.145.7956.1176.4126.593
Jun-975.1945.6125.9916.3086.429
Jul-975.2035.5055.665.8325.962
Aug-975.1855.6565.8746.136.252
Sep-975.025.5675.7125.9116.035
Oct-975.1735.3035.5675.6335.77
Nov-975.2575.4535.7115.7595.808
Dec-975.3075.4155.5785.6325.683
Jan-985.1585.1675.2635.315.491
Feb-985.2745.3335.4695.5125.54
Mar-985.1345.3185.5035.5445.574
Apr-984.9465.3335.5095.5625.602
May-984.9975.3575.4655.4855.461
Jun-985.0125.3415.4045.3855.346
Jul-985.0495.4395.4185.4675.419
Aug-984.8465.0284.8144.8655.047
Sep-984.3024.5724.2774.3474.443
Oct-984.3234.3994.1674.484.668
Nov-984.494.6354.4784.5624.664
Dec-984.4354.584.5194.5914.599
Jan-994.4374.4594.5314.5274.624
Feb-994.6424.8495.0975.2065.253
Mar-994.4534.6544.9385.1695.231
Apr-994.5184.7265.0115.2665.361
May-994.624.9165.3545.645.512
Jun-994.7345.1585.4565.7595.711
Jul-994.7135.2435.5595.9225.831
Aug-994.9065.4385.655.9685.863
Sep-994.8075.3765.555.8795.792
Oct-995.0455.4945.7236.0455.952
Nov-995.2495.7595.9316.1436.141
Dec-995.3275.8986.1486.396.387
Jan-005.6636.1696.5066.666.557
Feb-005.7356.1016.4416.5696.236
Mar-005.8276.3086.396.2536.047
Apr-005.86.4536.5676.4566.039
May-005.5756.276.5976.4536.116
Jun-005.8396.4116.286.1585.904
Jul-006.1946.3676.2046.1345.913
Aug-006.2566.1316.0875.9325.573
Sep-006.1666.2015.8855.7975.703
Oct-006.3086.2095.8245.7065.667
Nov-006.1625.8355.5485.3895.41
Dec-005.8495.4245.0514.9895.097
Jan-014.9664.6554.5674.8475.162
Feb-014.8334.4184.3864.6994.859
Mar-014.2664.1644.1864.624.919
Apr-013.8534.0364.2784.9385.372
May-013.6053.7924.2134.9775.436
Jun-013.6283.8824.2335.0675.477
Jul-013.5213.4583.7744.6715.166
Aug-013.3353.3343.6094.4974.844
Sep-012.3492.5172.8224.0554.682
Oct-012.0271.9572.373.6754.367
Nov-011.7822.0512.844.1034.911
Dec-011.6982.0533.0664.4475.206
Jan-021.7592.2783.1534.5195.205
Feb-021.7572.1973.0444.3584.93
Mar-021.7852.6893.6745.0035.46
Apr-021.7492.253.2164.5845.193
May-021.7222.273.1874.4145.187
Jun-021.6891.942.8754.1494.993
Jul-021.6931.7242.2233.6364.716
Aug-021.6671.7482.1093.2844.234
Sep-021.5431.4311.6812.6733.751
Oct-021.4361.3371.6652.8764.1
Nov-021.2191.5042.0393.3194.305
Dec-021.1871.2091.5822.8093.976
Jan-031.1691.2861.6913.0444.137
Feb-031.2051.2341.512.7263.805
Mar-031.1041.1451.4862.8253.948
Apr-031.1111.151.4772.8874.013
May-031.111.1631.3172.3513.483
Jun-030.8761.041.2992.5013.662
Jul-030.941.2261.7383.3624.59
Aug-030.9881.31.9613.5134.592
Sep-030.9281.0551.4622.884.122
Oct-030.9371.2391.8213.2964.492
Nov-030.9261.4492.0343.3874.458
Dec-030.9281.2281.8393.2644.42

Figure 2a. R2 in Regressions of Individual Macro Series on PCA Factors: First PCA Factor

Data for Figure 2a immediately follows.

Data for Figure 2a

CategoryMacro SeriesR2
110.582537
120.678626
130.881167
140.854461
150.808121
160.614026
170.580031
180.328113
190.643662
1100.849005
1110.834823
1120.598154
1130.891026
1140.006892
1150.035295
1160.478916
1170.823095
2180.25495
2190.244274
2200.729135
2210.7123
2220.142848
2230.243101
2240.37475
2250.692874
2260.665573
2270.703026
2280.517784
2290.512024
2300.752867
2310.787409
2320.017643
2330.738809
2340.723947
2350.721027
2360.559083
2370.511336
2380.557995
2390.37154
2400.535555
2410.197966
2420.014415
2430.789273
2440.359693
2450.485533
2460.42729
2470.63199
3480.439189
4490.865227
5500.538218
6510.463093
6520.216455
6530.259755
6540.339376
6550.448591
6560.465342
6570.283628
6580.301368
6590.317795
6600.421234
7610.479389
7620.265412
7630.379711
8640.630421
8650.442752
8660.470406
8670.675154
8680.766778
8690.631277
8700.276229
9710.043854
9720.0486
9730.003946
9740.012079
10750.051495
10760.006367
10770.12379
10780.007315
10790.00374
11800.018831
12810.001019
12820.010303
12830.028801
12840.135703
12850.012012
12860.000854
12870.062678
12880.029126
12890.10253
12900.305284
12910.217054
13920.106865
13930.071115
13940.047518
13950.040427
13960.169249
13970.306902
13980.112054
13990.168916
131000.055607
131010.106202
131020.359436
131030.088395
131040.117424
131050.250553
131060.222929
131070.149129
131080.156963
131090.145836
131100.127158
131110.078451
131120.169889
141130.059662
141140.098746
141150.042002
151160.01792

Figure 2b. R2 in Regressions of Individual Macro Series on PCA Factors: Second PCA Factor

Data for Figure 2b immediately follows.

Data for Figure 2b

CategoryMacro SeriesR2
110.01174
120.015714
130.008927
140.01957
150.03273
160.032822
170.100864
180.004863
190.144349
1100.00273
1110.001196
1120.007046
1130.002799
1140.000556
1150.001754
1160.014207
1170.001833
2180.12403
2190.242479
2200.16798
2210.168814
2220.000128
2230.115193
2240.058674
2250.000602
2260.042115
2270.014826
2280.06181
2290.047512
2300.150732
2310.130767
2320.413605
2330.00773
2340.164323
2350.164589
2360.122652
2370.248487
2380.260316
2390.437288
2400.178708
2410.166105
2420.063212
2430.078793
2440.112338
2450.030442
2460.113908
2470.071158
3480.16206
4490.002957
5500.08528
6510.002235
6520.01039
6530.001015
6540.007998
6550.004317
6560.048011
6577.79E-05
6580.044254
6590.095179
6600.004691
7610.165448
7620.229656
7630.154788
8640.002205
8650.029705
8660.046865
8670.016138
8680.000678
8690.032773
8700.215615
9710.097848
9720.084585
9730.258424
9740.344897
10750.003406
10760.006944
10770.004287
10780.000346
10790.003371
11800.476266
12810.000613
12820.026024
12830.119574
12840.234435
12850.00271
12860.004533
12870.030788
12880.220343
12890.071707
12900.08142
12910.045179
13920.757093
13930.735563
13940.734452
13950.235237
13960.246727
13970.23122
13980.46262
13990.774427
131000.535844
131010.590725
131020.224235
131030.819571
131040.538997
131050.560618
131060.670179
131070.78655
131080.786382
131090.755702
131100.549464
131110.792546
131120.53569
141130.58361
141140.370673
141150.59418
151160.070299

 

Figure 2c. R2 in Regressions of Individual Macro Series on PCA Factors: Third PCA Factor

Data for Figure 2c immediately follows.

Notes: The figure shows the R2 when regressing the individual series in the macro panel on each of the first three macro factors. The macro dataset consists of 116 series (transformed to ensure stationarity) and the sample period is January 1970 - December 2003 (408 monthly observations). Panels (a), (b) and (c) show the results for the first, second and third macro factor, respectively. In each panel the macro series are grouped according to the 15 categories as indicated on the horizontal axis. The group categories are (1) real output and income, (2) employment and hours, (3) real retail, (4) manufacturing and trade sales, (5) consumption, (6) housing starts and sales, (7) inventories, (8) orders, (9) stock prices, (10) exchange rates, (11) federal funds rate, (12) money and credit quantity aggregates, (13) prices indices, (14) average hourly earnings and (15) miscellaneous.

Data for Figure 2c

CategoryMacro SeriesR2
110.002729
120.014023
130.002397
142.46E-05
150.000581
160.073733
170.070968
180.038648
190.072469
1100.007217
1110.021144
1120.099038
1130.000339
1140.004627
1150.000813
1160.207427
1170.019485
2180.152216
2190.11109
2207.00E-09
2210.000165
2220.293521
2230.32993
2240.01164
2250.00065
2260.141167
2270.041864
2280.221495
2290.116388
2300.036199
2310.035093
2320.03288
2330.027329
2340.021692
2350.043128
2360.003684
2370.014206
2380.010553
2390.026035
2400.01037
2410.056579
2420.009334
2430.017269
2440.230765
2450.109662
2460.198815
2470.060418
3480.081042
4490.02703
5500.073724
6510.139286
6520.139055
6530.049224
6540.113621
6550.075943
6560.066691
6570.114031
6580.017335
6590.019903
6600.082107
7610.026003
7620.240743
7630.231277
8640.134934
8650.233122
8660.003455
8670.107107
8680.018083
8690.002261
8700.125456
9710.028848
9720.032151
9730.119848
9740.175055
10750.061502
10760.047285
10770.125467
10780.002926
10790.005079
11809.57E-06
12810.449035
12820.435628
12830.131709
12840.162051
12850.149093
12860.313409
12870.284221
12880.317046
12890.066629
12900.016485
12910.083199
13920.008585
13930.002158
13945.40E-05
13951.23E-06
13962.60E-05
13970.002709
13980.064146
13990.018131
131000.058521
131010.006305
131020.116481
131030.011257
131040.097492
131050.037911
131060.022317
131070.021465
131080.014828
131090.068837
131100.147954
131110.006868
131120.155201
141130.128055
141140.064399
141150.166552
151160.131223

Figure 3a. Macro Factors Compared to Individual Macro Series: First PCA Factor - IP:Total

Data for Figure 3a immediately follows.

Data for Figure 3a

MonthPCA FactorIP:Total
Jan-70-0.0020.089
Feb-70-0.143-0.034
Mar-70-0.180-0.068
Apr-70-0.225-0.113
May-70-0.288-0.108
Jun-70-0.280-0.095
Jul-70-0.296-0.159
Aug-70-0.301-0.173
Sep-70-0.370-0.193
Oct-70-0.407-0.226
Nov-70-0.490-0.328
Dec-70-0.520-0.311
Jan-71-0.381-0.185
Feb-71-0.274-0.055
Mar-71-0.233-0.061
Apr-71-0.197-0.060
May-71-0.119-0.020
Jun-71-0.0860.011
Jul-71-0.0500.048
Aug-71-0.0570.021
Sep-71-0.0280.001
Oct-710.0540.116
Nov-710.1600.252
Dec-710.2500.304
Jan-720.2430.248
Feb-720.2920.328
Mar-720.3300.387
Apr-720.3710.431
May-720.3860.451
Jun-720.4080.427
Jul-720.3940.417
Aug-720.4170.431
Sep-720.4930.517
Oct-720.5000.472
Nov-720.5490.499
Dec-720.5780.536
Jan-730.6000.547
Feb-730.5910.469
Mar-730.6100.487
Apr-730.5730.454
May-730.4970.392
Jun-730.4920.424
Jul-730.4910.417
Aug-730.4640.435
Sep-730.3900.367
Oct-730.3710.372
Nov-730.3310.339
Dec-730.2950.300
Jan-740.1620.220
Feb-740.0780.155
Mar-74-0.0130.069
Apr-74-0.0300.070
May-74-0.0670.085
Jun-74-0.1040.076
Jul-74-0.1530.068
Aug-74-0.2070.044
Sep-74-0.2490.008
Oct-74-0.379-0.032
Nov-74-0.495-0.086
Dec-74-0.684-0.267
Jan-75-0.841-0.434
Feb-75-0.924-0.463
Mar-75-0.996-0.556
Apr-75-1.071-0.617
May-75-1.000-0.619
Jun-75-0.977-0.656
Jul-75-0.929-0.618
Aug-75-0.838-0.562
Sep-75-0.727-0.474
Oct-75-0.615-0.416
Nov-75-0.531-0.384
Dec-75-0.393-0.209
Jan-76-0.1860.036
Feb-760.0100.163
Mar-760.1740.333
Apr-760.2450.386
May-760.2700.426
Jun-760.2920.456
Jul-760.2790.425
Aug-760.2470.400
Sep-760.2120.392
Oct-760.2100.340
Nov-760.1860.339
Dec-760.2240.399
Jan-770.2650.392
Feb-770.1380.296
Mar-770.1740.303
Apr-770.2410.368
May-770.2310.378
Jun-770.2620.396
Jul-770.2890.426
Aug-770.2860.416
Sep-770.2910.385
Oct-770.2940.400
Nov-770.3560.404
Dec-770.3260.332
Jan-780.3370.285
Feb-780.2550.251
Mar-780.2630.198
Apr-780.2970.227
May-780.3660.275
Jun-780.3500.264
Jul-780.3740.267
Aug-780.3410.251
Sep-780.3450.264
Oct-780.3320.253
Nov-780.3270.277
Dec-780.3440.311
Jan-790.2990.329
Feb-790.2970.361
Mar-790.2470.375
Apr-790.2390.296
May-790.0460.159
Jun-790.1050.168
Jul-790.0610.133
Aug-790.0320.119
Sep-79-0.0460.072
Oct-79-0.0500.062
Nov-79-0.1120.046
Dec-79-0.1810.006
Jan-80-0.218-0.018
Feb-80-0.2200.034
Mar-80-0.2560.010
Apr-80-0.419-0.019
May-80-0.493-0.076
Jun-80-0.720-0.231
Jul-80-0.714-0.295
Aug-80-0.679-0.312
Sep-80-0.562-0.266
Oct-80-0.485-0.187
Nov-80-0.410-0.156
Dec-80-0.365-0.065
Jan-81-0.358-0.042
Feb-81-0.397-0.099
Mar-81-0.427-0.119
Apr-81-0.337-0.079
May-81-0.203-0.001
Jun-81-0.0940.155
Jul-81-0.1050.245
Aug-81-0.1070.312
Sep-81-0.1490.292
Oct-81-0.2920.178
Nov-81-0.3920.089
Dec-81-0.492-0.052
Jan-82-0.567-0.136
Feb-82-0.652-0.195
Mar-82-0.532-0.083
Apr-82-0.566-0.144
May-82-0.596-0.163
Jun-82-0.612-0.232
Jul-82-0.645-0.273
Aug-82-0.649-0.327
Sep-82-0.690-0.365
Oct-82-0.622-0.354
Nov-82-0.621-0.359
Dec-82-0.571-0.322
Jan-83-0.485-0.307
Feb-83-0.312-0.130
Mar-83-0.343-0.249
Apr-83-0.267-0.176
May-83-0.186-0.070
Jun-83-0.0900.001
Jul-830.0260.047
Aug-830.1330.139
Sep-830.2020.237
Oct-830.2870.335
Nov-830.3880.416
Dec-830.4500.450
Jan-840.5070.521
Feb-840.5070.531
Mar-840.5990.569
Apr-840.5250.565
May-840.5220.529
Jun-840.5070.521
Jul-840.4860.508
Aug-840.4260.449
Sep-840.3740.402
Oct-840.2900.317
Nov-840.2490.270
Dec-840.2680.271
Jan-850.2250.245
Feb-850.1560.134
Mar-850.1210.144
Apr-850.1200.113
May-850.0840.082
Jun-850.0660.059
Jul-850.0430.042
Aug-850.021-0.004
Sep-850.0650.012
Oct-850.0990.045
Nov-850.0870.030
Dec-850.0500.028
Jan-860.0920.070
Feb-860.1340.113
Mar-860.0890.055
Apr-860.0820.016
May-860.1200.021
Jun-860.1140.025
Jul-860.0960.010
Aug-860.1220.070
Sep-860.1180.039
Oct-860.1120.028
Nov-860.1170.072
Dec-860.1130.081
Jan-870.1570.077
Feb-870.0850.021
Mar-870.1670.123
Apr-870.1720.169
May-870.1490.198
Jun-870.1840.217
Jul-870.2060.262
Aug-870.2090.266
Sep-870.2280.307
Oct-870.2050.308
Nov-870.2510.354
Dec-870.2590.356
Jan-880.2270.331
Feb-880.2480.361
Mar-880.2380.316
Apr-880.2400.317
May-880.2550.304
Jun-880.2040.274
Jul-880.2380.250
Aug-880.1910.230
Sep-880.1750.222
Oct-880.1680.196
Nov-880.1590.154
Dec-880.1630.140
Jan-890.1610.143
Feb-890.1710.154
Mar-890.1070.103
Apr-890.0720.108
May-890.0530.085
Jun-890.0070.056
Jul-89-0.0260.049
Aug-89-0.057-0.010
Sep-89-0.0460.008
Oct-89-0.0670.007
Nov-89-0.099-0.023
Dec-89-0.102-0.023
Jan-90-0.123-0.010
Feb-90-0.118-0.049
Mar-90-0.1090.019
Apr-90-0.1020.024
May-90-0.1420.028
Jun-90-0.1170.063
Jul-90-0.1170.078
Aug-90-0.1200.119
Sep-90-0.1850.088
Oct-90-0.2030.113
Nov-90-0.2500.082
Dec-90-0.3460.012
Jan-91-0.402-0.058
Feb-91-0.464-0.052
Mar-91-0.500-0.128
Apr-91-0.538-0.176
May-91-0.497-0.164
Jun-91-0.484-0.119
Jul-91-0.447-0.086
Aug-91-0.399-0.079
Sep-91-0.391-0.090
Oct-91-0.344-0.055
Nov-91-0.320-0.031
Dec-91-0.2650.022
Jan-92-0.2930.039
Feb-92-0.2360.030
Mar-92-0.1590.108
Apr-92-0.1060.172
May-92-0.0970.195
Jun-92-0.0840.163
Jul-92-0.1230.112
Aug-92-0.1280.150
Sep-92-0.1110.131
Oct-92-0.1370.095
Nov-92-0.0860.142
Dec-92-0.0590.174
Jan-930.0200.191
Feb-930.0160.238
Mar-930.0230.214
Apr-93-0.0400.184
May-93-0.0210.161
Jun-93-0.0210.125
Jul-93-0.0030.138
Aug-930.0010.119
Sep-930.0300.130
Oct-930.0580.152
Nov-930.0650.147
Dec-930.0890.144
Jan-940.1170.175
Feb-940.1100.181
Mar-940.0980.166
Apr-940.1930.204
May-940.1900.216
Jun-940.2410.264
Jul-940.2480.288
Aug-940.2330.277
Sep-940.2590.310
Oct-940.2630.289
Nov-940.2860.298
Dec-940.2930.307
Jan-950.2810.330
Feb-950.2930.325
Mar-950.2600.323
Apr-950.1970.280
May-950.1430.254
Jun-950.0980.234
Jul-950.0940.216
Aug-950.1010.187
Sep-950.0900.227
Oct-950.0990.242
Nov-950.0500.190
Dec-950.0310.177
Jan-960.0140.145
Feb-96-0.0710.089
Mar-960.0090.151
Apr-960.0050.139
May-960.0660.184
Jun-960.0860.210
Jul-960.1180.238
Aug-960.1290.254
Sep-960.1240.222
Oct-960.1200.228
Nov-960.1240.244
Dec-960.1470.273
Jan-970.1430.278
Feb-970.1780.329
Mar-970.1820.335
Apr-970.2050.360
May-970.2030.342
Jun-970.1960.324
Jul-970.1820.306
Aug-970.2170.342
Sep-970.2130.353
Oct-970.2260.365
Nov-970.2530.398
Dec-970.2800.386
Jan-980.2590.375
Feb-980.2900.383
Mar-980.2640.328
Apr-980.2430.327
May-980.2430.330
Jun-980.2450.336
Jul-980.2040.289
Aug-980.1590.246
Sep-980.2000.297
Oct-980.1670.249
Nov-980.1710.252
Dec-980.1340.203
Jan-990.1560.188
Feb-990.1660.194
Mar-990.1720.197
Apr-990.1750.202
May-990.1170.185
Jun-990.1550.194
Jul-990.1730.220
Aug-990.2060.259
Sep-990.1840.193
Oct-990.1650.191
Nov-990.1840.200
Dec-990.2090.240
Jan-000.2390.276
Feb-000.2290.243
Mar-000.2020.254
Apr-000.1900.255
May-000.2350.280
Jun-000.1710.277
Jul-000.1930.276
Aug-000.1430.227
Sep-000.0890.189
Oct-000.1140.219
Nov-000.0600.149
Dec-000.0220.119
Jan-01-0.0540.068
Feb-01-0.1190.027
Mar-01-0.142-0.028
Apr-01-0.175-0.069
May-01-0.226-0.119
Jun-01-0.253-0.174
Jul-01-0.314-0.209
Aug-01-0.285-0.206
Sep-01-0.302-0.211
Oct-01-0.392-0.263
Nov-01-0.395-0.254
Dec-01-0.393-0.275
Jan-02-0.383-0.272
Feb-02-0.323-0.199
Mar-02-0.268-0.165
Apr-02-0.266-0.125
May-02-0.244-0.091
Jun-02-0.202-0.058
Jul-02-0.1530.004
Aug-02-0.1570.019
Sep-02-0.1410.028
Oct-02-0.0890.053
Nov-02-0.1180.050
Dec-02-0.0890.081
Jan-03-0.0780.068
Feb-03-0.0620.065
Mar-03-0.1180.075
Apr-03-0.1190.019
May-03-0.149-0.031
Jun-03-0.123-0.042
Jul-03-0.129-0.075
Aug-03-0.098-0.032
Sep-03-0.086-0.028
Oct-03-0.0410.007
Nov-030.0110.040
Dec-030.0720.086

Figure 3b. Macro Factors Compared to Individual Macro Series: Second PCA Factor - CPI-U:Total

Data for Figure 3b immediately follows.

Data for Figure 3b

MonthPCA FactorCPI - U:Total
Jan-700.2160.048
Feb-700.2090.061
Mar-700.1830.073
Apr-700.1520.058
May-700.1520.056
Jun-700.1130.055
Jul-700.0690.054
Aug-700.0500.039
Sep-700.0200.039
Oct-700.0230.037
Nov-70-0.0060.036
Dec-70-0.0290.034
Jan-71-0.0570.033
Feb-71-0.0830.019
Mar-71-0.082-0.007
Apr-71-0.102-0.020
May-71-0.113-0.034
Jun-71-0.076-0.022
Jul-71-0.059-0.023
Aug-71-0.074-0.024
Sep-71-0.055-0.024
Oct-71-0.079-0.037
Nov-71-0.098-0.050
Dec-71-0.100-0.063
Jan-72-0.070-0.076
Feb-72-0.040-0.077
Mar-72-0.020-0.053
Apr-72-0.002-0.065
May-72-0.005-0.065
Jun-72-0.003-0.078
Jul-72-0.013-0.091
Aug-72-0.011-0.091
Sep-720.003-0.091
Oct-720.021-0.080
Nov-720.053-0.080
Dec-720.085-0.069
Jan-730.093-0.069
Feb-730.114-0.058
Mar-730.146-0.048
Apr-730.192-0.002
May-730.2320.020
Jun-730.2480.031
Jul-730.2950.053
Aug-730.2940.041
Sep-730.3650.118
Oct-730.3460.116
Nov-730.3880.148
Dec-730.4180.157
Jan-740.4390.189
Feb-740.4660.219
Mar-740.4710.237
Apr-740.4690.243
May-740.4730.240
Jun-740.4880.268
Jul-740.4930.275
Aug-740.5570.305
Sep-740.5440.276
Oct-740.5910.323
Nov-740.5780.319
Dec-740.5520.335
Jan-750.4720.330
Feb-750.3860.315
Mar-750.2880.291
Apr-750.2390.257
May-750.1760.245
Jun-750.1050.203
Jul-750.0550.200
Aug-750.0330.216
Sep-75-0.0120.174
Oct-75-0.0340.141
Nov-75-0.0480.130
Dec-75-0.0690.117
Jan-76-0.0510.106
Feb-76-0.0140.085
Mar-760.0400.066
Apr-760.0520.056
May-760.1090.046
Jun-760.1410.063
Jul-760.1420.052
Aug-760.1340.032
Sep-760.1220.040
Oct-760.1270.030
Nov-760.1200.028
Dec-760.1240.009
Jan-770.1470.008
Feb-770.1730.016
Mar-770.1900.057
Apr-770.2130.073
May-770.2240.097
Jun-770.2240.088
Jul-770.2490.086
Aug-770.2330.084
Sep-770.2410.083
Oct-770.2340.073
Nov-770.2420.071
Dec-770.2550.086
Jan-780.2600.085
Feb-780.2850.091
Mar-780.2630.064
Apr-780.2530.071
May-780.2890.076
Jun-780.3150.106
Jul-780.3340.120
Aug-780.3430.133
Sep-780.3540.139
Oct-780.3660.168
Nov-780.4030.188
Dec-780.4110.186
Jan-790.4220.191
Feb-790.4420.203
Mar-790.4630.229
Apr-790.4630.248
May-790.4670.258
Jun-790.4580.268
Jul-790.4580.285
Aug-790.4810.301
Sep-790.4760.319
Oct-790.4830.320
Nov-790.4750.329
Dec-790.4670.352
Jan-800.4770.381
Feb-800.4860.408
Mar-800.5150.420
Apr-800.5440.439
May-800.4950.439
Jun-800.4390.432
Jul-800.3880.425
Aug-800.3290.376
Sep-800.3340.365
Oct-800.3280.360
Nov-800.3190.354
Dec-800.3330.354
Jan-810.3310.341
Feb-810.3090.317
Mar-810.2640.299
Apr-810.2340.264
May-810.2430.243
Jun-810.2630.227
Jul-810.3050.223
Aug-810.3410.271
Sep-810.3400.273
Oct-810.3310.280
Nov-810.3060.249
Dec-810.2670.218
Jan-820.2250.187
Feb-820.2210.157
Mar-820.1460.128
Apr-820.0820.094
May-820.0470.082
Jun-820.0340.096
Jul-820.0150.108
Aug-82-0.0390.079
Sep-82-0.0890.052
Oct-82-0.1500.003
Nov-82-0.1820.008
Dec-82-0.229-0.018
Jan-83-0.248-0.049
Feb-83-0.274-0.055
Mar-83-0.268-0.066
Apr-83-0.272-0.061
May-83-0.234-0.041
Jun-83-0.253-0.068
Jul-83-0.263-0.114
Aug-83-0.239-0.120
Sep-83-0.188-0.115
Oct-83-0.125-0.100
Nov-83-0.098-0.101
Dec-83-0.046-0.081
Jan-84-0.005-0.051
Feb-840.032-0.027
Mar-840.073-0.008
Apr-840.1300.001
May-840.135-0.015
Jun-840.152-0.025
Jul-840.154-0.026
Aug-840.147-0.026
Sep-840.135-0.027
Oct-840.107-0.028
Nov-840.101-0.028
Dec-840.084-0.034
Jan-850.061-0.039
Feb-850.024-0.064
Mar-850.007-0.060
Apr-85-0.009-0.051
May-85-0.037-0.061
Jun-85-0.060-0.061
Jul-85-0.080-0.057
Aug-85-0.090-0.067
Sep-85-0.116-0.072
Oct-85-0.130-0.077
Nov-85-0.119-0.078
Dec-85-0.121-0.064
Jan-86-0.107-0.051
Feb-86-0.117-0.042
Mar-86-0.172-0.079
Apr-86-0.232-0.130
May-86-0.276-0.157
Jun-86-0.264-0.153
Jul-86-0.262-0.149
Aug-86-0.267-0.153
Sep-86-0.260-0.158
Oct-86-0.252-0.149
Nov-86-0.252-0.158
Dec-86-0.251-0.172
Jan-87-0.283-0.177
Feb-87-0.231-0.168
Mar-87-0.201-0.141
Apr-87-0.137-0.097
May-87-0.069-0.056
Jun-87-0.050-0.057
Jul-87-0.032-0.053
Aug-87-0.026-0.045
Sep-870.004-0.027
Oct-870.036-0.028
Nov-870.062-0.024
Dec-870.073-0.016
Jan-880.088-0.025
Feb-880.069-0.035
Mar-880.062-0.044
Apr-880.048-0.049
May-880.078-0.041
Jun-880.054-0.042
Jul-880.071-0.043
Aug-880.097-0.035
Sep-880.078-0.036
Oct-880.063-0.032
Nov-880.036-0.029
Dec-880.032-0.029
Jan-890.049-0.022
Feb-890.062-0.018
Mar-890.091-0.010
Apr-890.1020.001
May-890.0780.008
Jun-890.0890.019
Jul-890.0590.014
Aug-890.0220.009
Sep-89-0.009-0.012
Oct-89-0.022-0.020
Nov-89-0.018-0.013
Dec-89-0.022-0.010
Jan-90-0.021-0.011
Feb-90-0.0100.016
Mar-90-0.0130.019
Apr-90-0.0140.017
May-90-0.044-0.007
Jun-90-0.055-0.024
Jul-90-0.053-0.009
Aug-90-0.029-0.002
Sep-900.0190.039
Oct-900.0630.061
Nov-900.0720.071
Dec-900.0350.062
Jan-910.0250.065
Feb-91-0.0300.037
Mar-91-0.0950.021
Apr-91-0.144-0.002
May-91-0.162-0.003
Jun-91-0.1720.008
Jul-91-0.188-0.008
Aug-91-0.218-0.024
Sep-91-0.249-0.051
Oct-91-0.277-0.070
Nov-91-0.314-0.096
Dec-91-0.291-0.086
Jan-92-0.311-0.090
Feb-92-0.322-0.105
Mar-92-0.294-0.098
Apr-92-0.250-0.080
May-92-0.239-0.080
Jun-92-0.225-0.088
Jul-92-0.216-0.088
Aug-92-0.205-0.081
Sep-92-0.209-0.085
Oct-92-0.220-0.089
Nov-92-0.213-0.076
Dec-92-0.220-0.083
Jan-93-0.216-0.091
Feb-93-0.195-0.077
Mar-93-0.174-0.077
Apr-93-0.170-0.088
May-93-0.168-0.081
Jun-93-0.161-0.078
Jul-93-0.176-0.089
Aug-93-0.177-0.096
Sep-93-0.180-0.097
Oct-93-0.183-0.100
Nov-93-0.167-0.101
Dec-93-0.165-0.101
Jan-94-0.155-0.098
Feb-94-0.156-0.115
Mar-94-0.152-0.112
Apr-94-0.161-0.106
May-94-0.154-0.120
Jun-94-0.145-0.123
Jul-94-0.115-0.113
Aug-94-0.095-0.103
Sep-94-0.079-0.094
Oct-94-0.056-0.091
Nov-94-0.067-0.108
Dec-94-0.050-0.108
Jan-95-0.050-0.108
Feb-95-0.024-0.095
Mar-95-0.010-0.096
Apr-95-0.021-0.099
May-95-0.019-0.083
Jun-95-0.047-0.083
Jul-95-0.061-0.087
Aug-95-0.084-0.097
Sep-95-0.105-0.107
Oct-95-0.116-0.111
Nov-95-0.111-0.101
Dec-95-0.151-0.108
Jan-96-0.150-0.112
Feb-96-0.137-0.099
Mar-96-0.172-0.103
Apr-96-0.165-0.096
May-96-0.169-0.097
Jun-96-0.151-0.097
Jul-96-0.147-0.098
Aug-96-0.147-0.095
Sep-96-0.143-0.098
Oct-96-0.133-0.089
Nov-96-0.140-0.086
Dec-96-0.116-0.077
Jan-97-0.102-0.071
Feb-97-0.094-0.087
Mar-97-0.103-0.087
Apr-97-0.106-0.100
May-97-0.127-0.116
Jun-97-0.139-0.126
Jul-97-0.145-0.126
Aug-97-0.158-0.129
Sep-97-0.149-0.123
Oct-97-0.144-0.127
Nov-97-0.135-0.133
Dec-97-0.136-0.143
Jan-98-0.160-0.152
Feb-98-0.183-0.155
Mar-98-0.193-0.164
Apr-98-0.203-0.168
May-98-0.198-0.165
Jun-98-0.179-0.152
Jul-98-0.181-0.156
Aug-98-0.175-0.150
Sep-98-0.171-0.156
Oct-98-0.201-0.165
Nov-98-0.229-0.162
Dec-98-0.244-0.162
Jan-99-0.261-0.156
Feb-99-0.232-0.153
Mar-99-0.241-0.156
Apr-99-0.235-0.150
May-99-0.198-0.127
Jun-99-0.208-0.133
Jul-99-0.212-0.136
Aug-99-0.190-0.130
Sep-99-0.186-0.124
Oct-99-0.147-0.107
Nov-99-0.133-0.110
Dec-99-0.119-0.107
Jan-00-0.088-0.105
Feb-00-0.079-0.099
Mar-00-0.043-0.078
Apr-00-0.005-0.052
May-00-0.031-0.085
Jun-00-0.037-0.083
Jul-000.003-0.054
Aug-00-0.029-0.060
Sep-00-0.054-0.072
Oct-00-0.057-0.067
Nov-00-0.050-0.067
Dec-00-0.047-0.068
Jan-01-0.051-0.068
Feb-01-0.056-0.054
Mar-01-0.076-0.061
Apr-01-0.136-0.093
May-01-0.162-0.076
Jun-01-0.168-0.059
Jul-01-0.219-0.077
Aug-01-0.262-0.100
Sep-01-0.265-0.100
Oct-01-0.304-0.109
Nov-01-0.369-0.131
Dec-01-0.421-0.145
Jan-02-0.449-0.159
Feb-02-0.489-0.179
Mar-02-0.507-0.182
Apr-02-0.481-0.165
May-02-0.451-0.157
Jun-02-0.455-0.177
Jul-02-0.439-0.183
Aug-02-0.394-0.163
Sep-02-0.369-0.152
Oct-02-0.356-0.158
Nov-02-0.301-0.136
Dec-02-0.280-0.125
Jan-03-0.270-0.117
Feb-03-0.236-0.109
Mar-03-0.187-0.087
Apr-03-0.179-0.088
May-03-0.240-0.126
Jun-03-0.274-0.132
Jul-03-0.280-0.132
Aug-03-0.273-0.132
Sep-03-0.292-0.127
Oct-03-0.294-0.124
Nov-03-0.292-0.133
Dec-03-0.296-0.149

Figure 3c. Macro Factors Compared to Individual Macro Series: Third PCA Factor - M1

Data for Figure 3c immediately follows.

Notes: The figure shows time-series plots of the first three macro factors and the main individual macro series within the category to which the factor is most related. The first factor is plotted together with Industrial Production Index: Total Index (R2 is 0.88), the second factor is plotted with the Consumer Price Index: All Items (R2 is 0.77) and the third factor is plotted with Money Stock: M1 (R2 is 0.44). The macro dataset consists of 116 (transformed to ensure stationarity) series and the sample period used is January 1970 - December 2003 (408 monthly observations). The group categories are (1) real output and income, (2) employment and hours, (3) real retail, (4) manufacturing and trade sales, (5) consumption, (6) housing starts and sales, (7) inventories, (8) orders, (9) stock prices, (10) exchange rates, (11) federal funds rate, (12) money and credit quantity aggregates, (13) prices indices, (14) average hourly earnings and (15) miscellaneous.

Data for Figure 3c

MonthPCA FactorM1
Jan-70-0.137-0.107
Feb-70-0.165-0.084
Mar-70-0.143-0.127
Apr-70-0.141-0.128
May-70-0.137-0.121
Jun-70-0.096-0.112
Jul-70-0.042-0.114
Aug-70-0.020-0.115
Sep-70-0.016-0.070
Oct-700.005-0.035
Nov-700.028-0.029
Dec-700.034-0.027
Jan-710.141-0.018
Feb-710.184-0.049
Mar-710.2300.024
Apr-710.2420.039
May-710.2810.042
Jun-710.2860.075
Jul-710.2920.098
Aug-710.3030.120
Sep-710.2890.090
Oct-710.2700.065
Nov-710.2750.055
Dec-710.2620.049
Jan-720.2540.044
Feb-720.2740.058
Mar-720.2580.061
Apr-720.2390.072
May-720.2180.072
Jun-720.2070.034
Jul-720.1660.015
Aug-720.1700.030
Sep-720.1970.058
Oct-720.2200.085
Nov-720.2300.106
Dec-720.2320.122
Jan-730.2340.167
Feb-730.2090.173
Mar-730.1420.140
Apr-730.1260.088
May-730.0770.080
Jun-730.0710.117
Jul-730.0620.137
Aug-730.0020.106
Sep-73-0.0010.067
Oct-73-0.0070.024
Nov-73-0.0350.008
Dec-73-0.0380.018
Jan-74-0.117-0.002
Feb-74-0.121-0.031
Mar-74-0.094-0.016
Apr-74-0.0680.020
May-74-0.0370.009
Jun-74-0.062-0.026
Jul-74-0.051-0.044
Aug-74-0.067-0.045
Sep-74-0.071-0.034
Oct-74-0.104-0.022
Nov-74-0.113-0.019
Dec-74-0.132-0.032
Jan-75-0.103-0.059
Feb-75-0.089-0.081
Mar-75-0.032-0.089
Apr-75-0.025-0.090
May-750.064-0.103
Jun-750.118-0.057
Jul-750.180-0.017
Aug-750.233-0.009
Sep-750.254-0.017
Oct-750.296-0.005
Nov-750.289-0.034
Dec-750.328-0.035
Jan-760.342-0.039
Feb-760.358-0.012
Mar-760.3420.010
Apr-760.3220.017
May-760.2690.054
Jun-760.2210.021
Jul-760.189-0.031
Aug-760.155-0.037
Sep-760.165-0.014
Oct-760.143-0.032
Nov-760.1510.013
Dec-760.1480.015
Jan-770.1760.052
Feb-770.1370.063
Mar-770.1270.073
Apr-770.1680.079
May-770.1530.079
Jun-770.1570.077
Jul-770.1360.097
Aug-770.1420.102
Sep-770.1080.105
Oct-770.0980.128
Nov-770.1110.118
Dec-770.0910.125
Jan-780.0930.117
Feb-780.0670.135
Mar-780.0530.098
Apr-780.0540.085
May-780.0920.094
Jun-780.0920.148
Jul-780.0990.151
Aug-780.1040.140
Sep-780.0910.136
Oct-780.1130.139
Nov-780.0880.125
Dec-780.0780.121
Jan-790.0650.113
Feb-790.0420.079
Mar-790.0110.084
Apr-790.0290.094
May-79-0.0030.126
Jun-790.0010.075
Jul-79-0.0130.097
Aug-79-0.0320.138
Sep-79-0.0120.130
Oct-79-0.0220.100
Nov-79-0.0370.104
Dec-79-0.0190.075
Jan-80-0.0170.061
Feb-800.0000.095
Mar-800.0100.132
Apr-80-0.0630.076
May-80-0.062-0.059
Jun-80-0.101-0.067
Jul-80-0.022-0.063
Aug-800.057-0.051
Sep-800.135-0.007
Oct-800.1960.055
Nov-800.2470.087
Dec-800.2620.107
Jan-810.2050.068
Feb-810.1800.050
Mar-810.1750.037
Apr-810.2000.107
May-810.2220.266
Jun-810.2080.221
Jul-810.1290.172
Aug-810.0770.131
Sep-810.0280.065
Oct-81-0.042-0.004
Nov-81-0.090-0.038
Dec-81-0.144-0.026
Jan-82-0.1190.064
Feb-82-0.0750.097
Mar-82-0.1200.046
Apr-82-0.1030.007
May-82-0.099-0.043
Jun-82-0.075-0.017
Jul-82-0.057-0.014
Aug-82-0.024-0.028
Sep-82-0.0130.009
Oct-820.0410.069
Nov-820.0930.134
Dec-820.1510.175
Jan-830.1870.147
Feb-830.2250.105
Mar-830.3080.187
Apr-830.3160.241
May-830.3230.218
Jun-830.3470.291
Jul-830.3560.322
Aug-830.3700.352
Sep-830.3380.342
Oct-830.2920.304
Nov-830.2640.265
Dec-830.2250.207
Jan-840.2130.197
Feb-840.1540.207
Mar-840.1190.156
Apr-840.0380.129
May-840.0130.136
Jun-84-0.0460.084
Jul-84-0.0790.076
Aug-84-0.1190.046
Sep-84-0.1630.020
Oct-84-0.1840.017
Nov-84-0.186-0.020
Dec-84-0.1520.000
Jan-85-0.1470.012
Feb-85-0.1360.024
Mar-85-0.1070.060
Apr-85-0.1000.049
May-85-0.0830.049
Jun-85-0.0670.075
Jul-85-0.0260.105
Aug-85-0.0080.156
Sep-850.0350.214
Oct-850.0740.255
Nov-850.0770.286
Dec-850.0690.284
Jan-860.0910.310
Feb-860.1000.276
Mar-860.0920.247
Apr-860.0880.287
May-860.1070.310
Jun-860.1240.354
Jul-860.1270.358
Aug-860.1210.373
Sep-860.1350.375
Oct-860.1360.377
Nov-860.1270.396
Dec-860.1170.437
Jan-870.1610.506
Feb-870.1320.531
Mar-870.1440.506
Apr-870.1630.461
May-870.1440.473
Jun-870.1190.399
Jul-870.0900.314
Aug-870.0740.243
Sep-870.0830.195
Oct-870.0420.148
Nov-870.0210.150
Dec-870.0060.058
Jan-88-0.069-0.095
Feb-88-0.081-0.093
Mar-88-0.094-0.087
Apr-88-0.091-0.082
May-88-0.107-0.110
Jun-88-0.099-0.098
Jul-88-0.093-0.037
Aug-88-0.103-0.019
Sep-88-0.113-0.020
Oct-88-0.098-0.033
Nov-88-0.081-0.091
Dec-88-0.077-0.065
Jan-89-0.063-0.032
Feb-89-0.067-0.077
Mar-89-0.127-0.099
Apr-89-0.150-0.130
May-89-0.140-0.195
Jun-89-0.193-0.246
Jul-89-0.188-0.299
Aug-89-0.187-0.289
Sep-89-0.197-0.292
Oct-89-0.185-0.285
Nov-89-0.185-0.247
Dec-89-0.173-0.246
Jan-90-0.168-0.228
Feb-90-0.128-0.209
Mar-90-0.099-0.180
Apr-90-0.113-0.154
May-90-0.101-0.098
Jun-90-0.082-0.081
Jul-90-0.077-0.045
Aug-90-0.093-0.066
Sep-90-0.090-0.040
Oct-90-0.099-0.023
Nov-90-0.108-0.063
Dec-90-0.109-0.058
Jan-91-0.159-0.071
Feb-91-0.158-0.072
Mar-91-0.129-0.056
Apr-91-0.112-0.042
May-91-0.087-0.048
Jun-91-0.0540.000
Jul-91-0.0270.021
Aug-91-0.0060.037
Sep-910.0030.032
Oct-910.0070.027
Nov-910.0250.074
Dec-910.0220.111
Jan-920.0290.148
Feb-920.0350.208
Mar-920.0770.255
Apr-920.0840.281
May-920.0630.297
Jun-920.0750.292
Jul-920.0520.264
Aug-920.0490.286
Sep-920.0450.311
Oct-920.0300.359
Nov-920.0440.394
Dec-920.0490.404
Jan-930.0760.394
Feb-930.0450.345
Mar-930.0090.281
Apr-93-0.0390.244
May-93-0.0580.248
Jun-93-0.0500.302
Jul-93-0.0540.323
Aug-93-0.0630.318
Sep-93-0.0490.309
Oct-93-0.0470.286
Nov-93-0.0490.245
Dec-93-0.0480.232
Jan-94-0.0450.215
Feb-94-0.0650.199
Mar-94-0.0230.203
Apr-94-0.0180.197
May-94-0.0420.155
Jun-94-0.0540.079
Jul-94-0.0630.047
Aug-94-0.0750.023
Sep-94-0.078-0.021
Oct-94-0.095-0.062
Nov-94-0.111-0.104
Dec-94-0.137-0.152
Jan-95-0.168-0.178
Feb-95-0.188-0.184
Mar-95-0.221-0.221
Apr-95-0.240-0.241
May-95-0.233-0.230
Jun-95-0.231-0.260
Jul-95-0.255-0.275
Aug-95-0.226-0.287
Sep-95-0.240-0.288
Oct-95-0.242-0.313
Nov-95-0.267-0.327
Dec-95-0.238-0.340
Jan-96-0.240-0.369
Feb-96-0.210-0.390
Mar-96-0.233-0.392
Apr-96-0.215-0.373
May-96-0.175-0.376
Jun-96-0.188-0.391
Jul-96-0.174-0.393
Aug-96-0.183-0.414
Sep-96-0.197-0.463
Oct-96-0.192-0.469
Nov-96-0.187-0.489
Dec-96-0.184-0.498
Jan-97-0.181-0.481
Feb-97-0.183-0.455
Mar-97-0.175-0.450
Apr-97-0.215-0.501
May-97-0.227-0.548
Jun-97-0.219-0.510
Jul-97-0.224-0.495
Aug-97-0.187-0.474
Sep-97-0.193-0.394
Oct-97-0.195-0.397
Nov-97-0.181-0.359
Dec-97-0.186-0.326
Jan-98-0.184-0.298
Feb-98-0.187-0.300
Mar-98-0.182-0.266
Apr-98-0.167-0.238
May-98-0.172-0.202
Jun-98-0.197-0.204
Jul-98-0.210-0.216
Aug-98-0.221-0.225
Sep-98-0.216-0.265
Oct-98-0.205-0.210
Nov-98-0.177-0.180
Dec-98-0.167-0.157
Jan-99-0.152-0.159
Feb-99-0.149-0.166
Mar-99-0.138-0.181
Apr-99-0.131-0.172
May-99-0.134-0.156
Jun-99-0.101-0.157
Jul-99-0.066-0.161
Aug-99-0.083-0.163
Sep-99-0.085-0.157
Oct-99-0.094-0.186
Nov-99-0.099-0.193
Dec-99-0.099-0.190
Jan-00-0.090-0.143
Feb-00-0.093-0.157
Mar-00-0.134-0.213
Apr-00-0.127-0.215
May-00-0.152-0.219
Jun-00-0.162-0.249
Jul-00-0.202-0.242
Aug-00-0.188-0.243
Sep-00-0.205-0.248
Oct-00-0.192-0.257
Nov-00-0.222-0.278
Dec-00-0.237-0.345
Jan-01-0.265-0.429
Feb-01-0.252-0.379
Mar-01-0.224-0.308
Apr-01-0.209-0.272
May-01-0.187-0.273
Jun-01-0.182-0.219
Jul-01-0.129-0.181
Aug-01-0.098-0.123
Sep-01-0.060-0.065
Oct-010.0310.166
Nov-01-0.0100.007
Dec-010.0270.051
Jan-020.0380.124
Feb-020.0880.113
Mar-020.1320.103
Apr-020.1440.081
May-020.1400.023
Jun-020.1510.019
Jul-020.1300.002
Aug-020.097-0.024
Sep-020.067-0.123
Oct-020.037-0.310
Nov-020.019-0.106
Dec-020.039-0.109
Jan-030.071-0.110
Feb-030.042-0.120
Mar-030.015-0.070
Apr-03-0.010-0.064
May-03-0.0170.002
Jun-030.0270.031
Jul-030.0490.065
Aug-030.0630.058
Sep-030.1060.139
Oct-030.1170.111
Nov-030.0990.069
Dec-030.1060.056

Figure 4a. Trace Cumulative Squared Prediction Errors, 1-Month Forecast Horizon, 1989 - 2003: Yield-Only Models

Data for Figure 4a immediately follows.

Data for Figure 4a

MonthARVARNS2-ARNS2-VARNS1ATSM
Jan-89-0.0120.2520.1420.3010.709-0.073
Feb-890.0660.248-0.791-0.355-0.226-0.233
Mar-890.0420.229-1.236-0.2600.960-0.771
Apr-890.1610.6800.0520.5291.981-0.272
May-890.0860.4520.3690.6052.454-0.624
Jun-89-0.023-0.7200.526-0.0032.245-1.680
Jul-89-0.264-2.455-0.535-1.4721.913-3.419
Aug-890.223-0.1171.7120.9363.667-1.066
Sep-890.259-0.1221.7190.9963.605-1.065
Oct-890.048-0.7341.7720.7024.208-1.679
Nov-89-0.020-1.2001.4910.2453.949-2.077
Dec-890.058-1.0761.5040.2813.903-2.015
Jan-900.335-0.4871.7860.7494.325-1.556
Feb-900.380-0.4501.8900.8934.295-1.552
Mar-900.444-0.3672.0221.0674.317-1.447
Apr-900.5740.0032.1071.2703.988-1.086
May-900.4930.1372.5621.5874.595-0.978
Jun-900.409-0.0632.5141.4914.553-1.247
Jul-900.298-0.6072.0971.0013.738-1.838
Aug-900.4780.2072.8431.7584.153-1.130
Sep-900.421-0.2972.1241.1613.711-1.691
Oct-900.311-0.9991.0650.2712.993-2.318
Nov-900.132-1.969-0.494-1.0451.446-3.293
Dec-90-0.182-2.771-1.954-2.293-1.395-4.127
Jan-91-0.343-3.076-2.553-2.678-2.243-4.493
Feb-91-0.487-3.384-3.295-3.135-2.777-4.929
Mar-91-0.566-3.457-3.533-3.197-3.032-5.212
Apr-91-0.834-3.967-4.466-3.712-3.180-5.953
May-91-0.847-4.029-4.753-3.819-3.289-6.206
Jun-91-0.752-3.807-4.582-3.624-3.241-6.252
Jul-91-0.867-4.171-5.393-4.043-3.670-6.701
Aug-91-1.356-5.537-7.974-5.605-5.532-8.040
Sep-91-1.870-7.246-11.105-7.518-7.919-9.637
Oct-91-2.273-8.398-13.313-8.798-9.882-10.910
Nov-91-2.963-10.170-17.033-10.817-12.127-12.518
Dec-91-4.105-13.185-23.633-14.425-12.044-15.124
Jan-92-3.598-11.976-21.894-13.028-11.077-14.301
Feb-92-3.528-12.040-22.726-13.135-11.570-14.540
Mar-92-3.153-11.295-21.896-12.438-10.797-14.288
Apr-92-3.644-11.895-23.566-12.922-11.471-15.290
May-92-3.986-12.609-25.823-13.709-12.398-15.968
Jun-92-4.494-13.737-28.677-14.807-14.043-16.959
Jul-92-5.469-15.783-33.733-16.890-17.018-18.773
Aug-92-5.846-16.828-36.377-17.863-18.564-19.506
Sep-92-6.710-18.762-41.086-19.652-19.360-20.965
Oct-92-5.885-17.198-38.486-17.927-17.664-19.661
Nov-92-5.370-16.500-37.440-17.206-16.798-19.236
Dec-92-5.888-17.157-39.600-17.812-17.856-20.028
Jan-93-6.553-18.133-42.425-18.613-19.294-20.764
Feb-93-7.084-19.288-45.383-19.637-20.646-21.522
Mar-93-7.139-19.531-46.377-19.793-21.215-21.662
Apr-93-7.383-20.180-48.048-20.324-22.029-22.108
May-93-7.036-19.744-47.624-19.809-21.579-21.660
Jun-93-7.578-20.760-50.111-20.705-22.813-22.430
Jul-93-7.564-20.800-50.498-20.713-23.082-22.525
Aug-93-8.075-21.646-52.421-21.417-23.593-23.150
Sep-93-8.246-21.977-53.214-21.679-24.189-23.456
Oct-93-8.179-21.972-53.405-21.663-24.297-23.464
Nov-93-7.786-21.468-52.679-21.255-24.148-23.066
Dec-93-7.931-21.717-53.368-21.465-24.596-23.326
Jan-94-8.263-22.187-54.527-21.836-25.093-23.741
Feb-94-7.371-21.066-52.546-20.885-24.120-22.926
Mar-94-6.656-20.468-51.036-20.405-23.853-22.669
Apr-94-6.093-20.178-50.010-20.153-23.832-22.625
May-94-5.827-20.152-49.762-20.193-23.828-22.711
Jun-94-5.753-20.476-49.898-20.598-24.532-23.183
Jul-94-5.877-20.234-50.014-20.415-24.430-22.998
Aug-94-5.671-20.091-49.749-20.250-24.210-22.949
Sep-94-5.272-20.076-49.305-20.292-24.451-23.066
Oct-94-5.084-20.200-49.257-20.486-24.732-23.268
Nov-94-4.684-20.144-48.940-20.418-24.240-23.311
Dec-94-4.685-20.486-49.469-21.019-24.962-23.755
Jan-95-4.705-19.483-48.657-20.110-24.133-22.813
Feb-95-4.958-19.223-48.283-19.894-23.835-22.635
Mar-95-4.951-19.216-48.221-19.823-23.791-22.664
Apr-95-5.093-19.422-48.345-19.976-23.803-22.914
May-95-5.663-20.354-49.147-20.823-24.071-23.869
Jun-95-5.835-20.793-49.490-21.250-24.660-24.254
Jul-95-5.691-20.568-49.296-21.041-24.591-24.034
Aug-95-5.838-20.998-49.663-21.387-24.759-24.440
Sep-95-5.931-21.284-49.865-21.608-24.897-24.738
Oct-95-6.145-21.676-50.174-22.001-25.207-25.148
Nov-95-6.407-22.273-50.594-22.473-25.572-25.782
Dec-95-6.788-23.022-51.186-23.254-26.548-26.435
Jan-96-6.912-23.214-51.303-23.394-26.932-26.600
Feb-96-6.433-22.060-50.173-22.325-26.205-25.439
Mar-96-6.106-21.566-49.552-21.778-25.908-24.996
Apr-96-5.935-21.222-49.167-21.473-25.788-24.663
May-96-5.767-21.143-48.983-21.348-25.820-24.642
Jun-96-5.918-21.245-49.090-21.419-25.732-24.804
Jul-96-5.807-21.167-49.025-21.347-25.691-24.781
Aug-96-5.727-21.187-48.969-21.338-25.791-24.838
Sep-96-5.964-21.421-49.163-21.498-25.703-25.129
Oct-96-6.258-21.632-49.421-21.641-25.609-25.394
Nov-96-6.494-22.000-49.771-21.935-25.825-25.804
Dec-96-6.230-21.618-49.432-21.619-25.628-25.434
Jan-97-6.209-21.632-49.416-21.610-25.664-25.486
Feb-97-6.115-21.591-49.305-21.510-25.625-25.522
Mar-97-5.813-21.430-49.122-21.348-25.682-25.403
Apr-97-5.971-21.527-49.139-21.387-25.527-25.569
May-97-6.085-21.634-49.215-21.537-25.662-25.686
Jun-97-6.183-21.609-49.102-21.401-25.553-25.743
Jul-97-6.507-21.874-49.284-21.524-25.399-26.052
Aug-97-6.290-21.623-49.096-21.317-25.292-25.755
Sep-97-6.534-21.895-49.218-21.539-25.342-26.058
Oct-97-6.718-21.971-49.230-21.541-25.262-26.208
Nov-97-6.638-21.943-49.195-21.462-25.201-26.259
Dec-97-6.759-22.099-49.217-21.535-25.218-26.492
Jan-98-7.077-22.582-49.321-21.900-25.524-26.988
Feb-98-6.920-22.408-49.182-21.687-25.372-26.884
Mar-98-6.916-22.537-49.149-21.687-25.388-26.964
Apr-98-7.004-22.643-49.055-21.761-25.309-27.016
May-98-7.096-22.752-49.138-21.922-25.550-27.183
Jun-98-7.146-22.701-49.031-21.778-25.514-27.194
Jul-98-7.165-22.743-49.040-21.849-25.617-27.229
Aug-98-7.718-23.140-48.846-22.099-25.804-27.693
Sep-98-8.519-24.464-49.392-23.289-27.160-28.954
Oct-98-8.532-24.483-49.481-23.438-27.610-28.935
Nov-98-8.246-24.101-49.240-23.084-27.154-28.695
Dec-98-8.305-24.277-49.272-23.179-27.333-28.886
Jan-99-8.389-24.473-49.298-23.258-27.451-29.064
Feb-99-7.729-23.498-48.824-22.491-26.989-28.141
Mar-99-7.882-23.804-48.873-22.641-27.049-28.400
Apr-99-7.851-23.811-48.802-22.577-27.034-28.479
May-99-7.554-23.587-48.591-22.377-27.004-28.372
Jun-99-7.447-23.523-48.611-22.361-27.000-28.371
Jul-99-7.381-23.634-48.642-22.437-27.129-28.522
Aug-99-7.265-23.608-48.759-22.506-27.296-28.572
Sep-99-7.393-23.721-48.767-22.567-27.472-28.721
Oct-99-7.278-23.705-48.885-22.661-27.590-28.777
Nov-99-7.077-23.583-49.069-22.657-27.401-28.702
Dec-99-6.895-23.552-49.226-22.688-27.406-28.680
Jan-00-6.695-23.507-49.295-22.581-27.290-28.700
Feb-00-6.733-23.540-49.232-22.497-27.203-28.802
Mar-00-6.829-23.452-49.011-22.247-27.024-28.878
Apr-00-6.764-23.580-49.237-22.385-27.160-28.904
May-00-6.836-23.888-49.506-22.916-27.702-29.144
Jun-00-6.831-22.712-48.896-21.824-26.357-28.094
Jul-00-6.808-22.574-49.054-21.652-26.056-28.087
Aug-00-6.941-22.894-48.995-21.799-26.134-28.443
Sep-00-7.000-22.923-48.900-21.881-26.260-28.479
Oct-00-7.033-23.076-49.032-22.025-26.328-28.810
Nov-00-7.274-23.824-49.199-22.683-27.083-29.666
Dec-00-7.631-24.917-49.567-23.723-28.385-30.745
Jan-01-8.032-25.629-49.771-24.354-29.557-31.045
Feb-01-8.228-26.342-50.358-24.920-29.980-31.739
Mar-01-8.540-26.866-50.914-25.324-29.573-32.004
Apr-01-8.521-26.213-50.373-24.712-28.952-31.333
May-01-8.727-26.413-50.729-24.842-29.258-31.633
Jun-01-8.721-26.423-50.797-24.839-29.251-31.797
Jul-01-9.130-27.093-51.962-25.376-29.727-32.496
Aug-01-9.439-27.776-53.120-25.952-30.200-33.211
Sep-01-10.503-29.278-55.612-27.048-31.646-34.570
Oct-01-11.222-30.665-58.410-28.186-33.081-35.849
Nov-01-10.988-29.455-57.085-27.141-31.947-35.273
Dec-01-10.851-29.219-56.765-26.989-31.712-35.714
Jan-02-10.815-29.199-57.031-27.021-31.744-36.147
Feb-02-11.011-29.459-57.927-27.212-31.968-36.738
Mar-02-10.448-28.742-56.278-26.765-31.234-36.916
Apr-02-10.908-28.980-57.431-26.837-31.328-37.562
May-02-11.062-29.152-58.079-26.929-31.438-38.029
Jun-02-11.417-29.633-59.488-27.310-31.774-38.698
Jul-02-11.915-30.569-61.813-28.006-32.534-39.302
Aug-02-12.241-31.732-64.202-28.967-33.578-40.093
Sep-02-12.868-33.628-67.680-30.456-35.752-41.325
Oct-02-12.876-33.547-67.985-30.308-36.022-41.129
Nov-02-12.688-32.467-67.032-29.301-35.532-40.350
Dec-02-13.237-33.831-70.029-30.353-36.882-41.102
Jan-03-13.146-33.637-70.070-30.098-36.835-40.929
Feb-03-13.415-34.713-72.191-30.893-37.773-41.533
Mar-03-13.470-34.865-72.826-30.922-38.117-41.568
Apr-03-13.512-35.153-73.604-31.051-38.436-41.705
May-03-13.886-36.742-76.448-32.234-39.904-42.581
Jun-03-14.018-36.855-77.160-32.283-40.628-42.547
Jul-03-13.422-35.173-74.460-30.898-39.577-41.419
Aug-03-13.332-35.017-74.609-30.723-39.475-41.386
Sep-03-13.887-36.301-77.809-31.667-40.789-42.043
Oct-03-13.595-35.543-76.745-30.983-40.139-41.579
Nov-03-13.540-35.452-76.917-30.859-40.093-41.580
Dec-03-13.738-35.802-78.051-31.102-40.451-41.839

Figure 4b. Trace Cumulative Squared Prediction Errors, 1-Month Forecast Horizon, 1989 - 2003: Macro Models

Data for Figure 4b immediately follows.

Data for Figure 4b

MonthAR-XVAR-XNS2-AR-XNS2-VAR-XNS1-XATSM-X
Jan-890.1580.238-0.1610.0260.6750.337
Feb-890.399-0.069-1.746-1.401-0.6140.321
Mar-890.543-0.622-2.925-2.1430.218-0.167
Apr-890.6840.530-1.266-0.6741.6280.804
May-890.8050.734-0.770-0.2192.2251.060
Jun-890.8541.0300.2650.6622.7350.995
Jul-891.0520.529-0.1790.3152.7780.205
Aug-89-0.3780.6281.3211.6034.0153.363
Sep-89-0.4910.2970.9701.2753.8133.380
Oct-89-0.3670.8761.9382.2784.5003.395
Nov-89-0.3561.0342.2062.5514.5702.618
Dec-89-0.4480.8171.8272.1224.4402.508
Jan-90-0.8260.0920.8331.0334.1651.732
Feb-90-0.991-0.2270.5070.7244.0051.551
Mar-90-1.228-0.5410.1510.3723.6861.177
Apr-90-1.089-0.348-0.505-0.2812.8871.330
May-90-1.1400.0840.5040.7013.8642.358
Jun-90-0.9130.2520.6760.9144.0102.373
Jul-90-0.9620.1710.8391.1183.9531.835
Aug-90-0.9280.8441.2601.5054.1662.784
Sep-90-0.7920.5620.9321.2173.9992.760
Oct-90-0.6070.0170.1590.5343.6161.985
Nov-90-0.468-0.905-1.236-0.6502.5531.043
Dec-900.076-0.893-2.371-1.4060.5640.443
Jan-910.266-0.808-2.726-1.557-0.0320.568
Feb-910.356-0.663-3.141-1.723-0.3860.390
Mar-910.219-0.643-3.108-1.606-0.4040.488
Apr-910.389-0.695-3.328-1.610-0.3940.565
May-910.271-0.746-3.359-1.648-0.4720.421
Jun-910.270-0.526-3.153-1.522-0.4120.450
Jul-910.275-0.943-3.469-1.739-0.5470.405
Aug-910.324-2.227-4.755-2.645-1.604-0.366
Sep-910.441-3.684-6.458-3.881-3.162-3.179
Oct-910.739-3.989-7.280-4.375-4.367-3.449
Nov-911.090-4.858-8.967-5.460-6.355-4.944
Dec-912.416-6.082-12.437-8.016-9.480-8.505
Jan-921.948-5.096-10.919-6.825-8.617-6.829
Feb-921.494-5.217-11.078-6.887-8.584-7.334
Mar-921.022-4.683-10.341-6.308-7.921-6.610
Apr-920.868-5.521-11.034-6.648-8.117-6.668
May-920.909-6.575-12.467-7.665-8.671-7.791
Jun-921.341-7.119-14.225-8.874-9.909-8.862
Jul-922.032-8.685-17.722-11.274-12.556-10.701
Aug-922.205-9.157-19.336-12.254-13.780-12.506
Sep-922.876-10.341-22.569-14.254-16.635-15.414
Oct-922.436-8.650-20.210-12.357-15.054-13.193
Nov-921.861-8.182-19.232-11.623-14.248-12.683
Dec-921.415-9.634-20.455-12.247-15.196-13.146
Jan-931.263-10.987-22.077-13.090-16.501-14.219
Feb-930.765-13.104-24.041-14.253-17.936-17.076
Mar-930.740-13.252-24.485-14.389-18.434-18.164
Apr-930.722-13.480-25.393-14.854-19.053-19.401
May-93-0.587-13.817-24.814-14.370-18.614-19.254
Jun-93-0.108-13.963-25.816-14.786-19.346-20.061
Jul-93-0.157-13.949-25.796-14.759-19.423-20.341
Aug-930.009-14.170-26.202-14.756-19.736-20.891
Sep-930.008-14.218-26.260-14.751-19.995-21.254
Oct-93-0.003-14.248-26.283-14.876-20.076-21.600
Nov-93-0.101-14.230-26.279-15.204-20.301-21.707
Dec-93-0.117-14.291-26.363-15.223-20.518-21.867
Jan-94-0.061-14.349-26.545-15.186-20.582-21.889
Feb-940.141-13.897-26.043-15.440-20.557-22.502
Mar-94-0.210-14.428-26.131-16.157-21.155-24.237
Apr-940.138-14.231-26.077-16.564-21.599-25.430
May-940.556-14.088-26.434-17.109-21.947-27.197
Jun-940.422-14.881-27.085-17.907-22.844-29.181
Jul-940.504-14.486-26.792-17.565-22.505-29.200
Aug-940.534-14.677-26.945-17.810-22.644-30.487
Sep-940.406-15.444-27.622-18.705-23.823-33.131
Oct-940.556-15.718-28.132-19.330-24.483-33.942
Nov-940.892-15.932-28.646-19.976-24.703-35.446
Dec-940.875-16.713-29.720-21.035-25.680-37.724
Jan-951.007-15.694-28.966-20.086-24.440-38.237
Feb-951.453-14.434-27.726-18.920-23.226-36.742
Mar-951.446-14.551-27.912-19.040-23.310-37.402
Apr-951.529-14.407-27.703-18.822-23.058-37.271
May-952.444-13.264-26.539-17.752-21.763-36.389
Jun-952.458-13.183-26.361-17.586-21.780-36.260
Jul-952.384-13.257-26.738-17.925-22.037-36.829
Aug-952.403-13.323-26.691-17.884-21.916-36.967
Sep-952.393-13.385-26.766-17.947-21.918-37.511
Oct-952.334-13.301-26.617-17.777-21.742-37.404
Nov-952.415-13.181-26.473-17.565-21.406-37.217
Dec-952.787-12.548-25.784-16.939-21.029-36.590
Jan-962.825-12.442-25.814-16.871-20.839-36.565
Feb-962.910-11.991-26.099-17.298-21.114-36.119
Mar-962.820-12.180-26.388-17.720-21.706-36.442
Apr-962.826-12.144-26.757-18.118-22.166-36.856
May-962.736-12.580-27.386-18.755-22.926-37.882
Jun-962.568-12.540-27.206-18.568-22.729-37.940
Jul-962.682-12.594-27.691-19.024-23.127-39.069
Aug-962.649-12.903-28.146-19.448-23.645-39.886
Sep-962.748-12.618-27.726-19.042-23.168-39.561
Oct-962.998-12.088-27.201-18.481-22.579-39.022
Nov-963.105-11.924-27.013-18.274-22.371-39.317
Dec-963.065-12.197-27.664-18.896-22.711-39.585
Jan-973.072-12.220-27.866-19.082-22.871-39.924
Feb-973.067-12.404-28.113-19.334-23.218-40.439
Mar-973.120-12.844-28.955-20.160-24.131-41.837
Apr-973.143-12.658-28.683-19.897-23.832-41.810
May-973.176-12.606-28.664-19.888-23.817-42.114
Jun-973.282-12.474-28.518-19.680-23.541-42.220
Jul-973.515-11.929-27.797-18.969-22.915-41.038
Aug-973.335-12.405-28.737-19.743-23.470-41.699
Sep-973.290-12.208-28.338-19.392-23.107-41.422
Oct-973.206-11.988-28.134-19.109-22.764-41.155
Nov-973.192-12.282-28.710-19.534-23.017-41.743
Dec-973.171-12.216-28.753-19.470-22.900-41.932
Jan-983.076-11.957-28.202-18.967-22.490-41.315
Feb-982.925-12.371-28.851-19.417-22.696-41.698
Mar-982.892-12.478-29.254-19.646-22.787-42.016
Apr-982.911-12.394-29.228-19.578-22.648-42.012
May-982.938-12.483-29.527-19.757-22.737-42.239
Jun-982.962-12.390-29.794-19.799-22.534-42.209
Jul-982.941-12.571-30.237-20.088-22.701-42.735
Aug-983.817-10.949-28.741-18.761-21.655-40.783
Sep-984.431-9.815-27.321-17.631-21.200-39.356
Oct-984.389-9.964-27.785-18.011-21.434-39.729
Nov-984.145-10.532-28.505-18.619-21.494-40.450
Dec-984.138-10.563-28.717-18.760-21.543-40.660
Jan-994.134-10.580-28.957-18.882-21.532-40.885
Feb-994.013-11.220-30.839-20.311-22.322-42.051
Mar-993.928-11.208-30.799-20.226-22.276-42.038
Apr-993.849-11.388-31.051-20.389-22.611-42.337
May-993.815-11.742-31.941-21.102-23.182-43.478
Jun-993.744-12.101-32.543-21.582-23.517-44.160
Jul-993.712-12.437-33.042-21.993-23.771-44.716
Aug-993.875-12.468-33.689-22.496-24.164-45.089
Sep-993.776-12.424-33.629-22.427-24.185-45.052
Oct-993.585-13.034-34.248-22.925-24.578-45.904
Nov-993.643-13.417-35.034-23.514-24.642-46.311
Dec-993.554-13.992-35.782-24.073-24.953-46.810
Jan-003.671-14.273-36.404-24.494-25.179-47.364
Feb-003.635-14.272-36.382-24.409-25.119-47.398
Mar-003.633-14.065-36.098-24.072-24.925-47.172
Apr-003.634-14.408-36.608-24.458-25.119-47.375
May-003.607-14.613-36.948-24.899-25.473-47.538
Jun-003.748-13.646-36.450-24.024-24.037-46.712
Jul-003.701-13.856-36.914-24.195-23.874-46.972
Aug-003.667-13.896-36.777-24.080-23.784-46.993
Sep-003.757-13.688-36.657-23.952-23.677-46.836
Oct-003.748-13.835-36.945-24.158-23.678-47.100
Nov-003.555-14.129-36.719-24.120-23.881-47.249
Dec-003.544-14.306-36.391-24.004-24.203-47.177
Jan-014.332-13.195-35.680-23.302-23.999-46.490
Feb-014.452-13.440-36.019-23.523-24.107-46.646
Mar-014.622-13.334-36.094-23.326-23.925-46.199
Apr-014.659-12.672-35.438-22.694-23.344-45.548
May-014.707-12.597-35.481-22.583-23.480-45.399
Jun-014.704-12.587-35.482-22.623-23.493-45.528
Jul-014.750-12.813-35.941-22.617-23.541-44.998
Aug-014.883-12.996-36.422-22.792-23.709-45.168
Sep-014.265-13.990-36.784-22.359-24.413-44.425
Oct-013.710-15.484-38.381-22.946-25.199-44.856
Nov-013.845-14.281-37.020-21.949-24.059-44.155
Dec-013.604-14.262-36.732-21.926-23.826-43.974
Jan-023.431-14.367-36.828-22.079-23.984-44.152
Feb-023.497-14.317-37.021-22.143-24.150-44.329
Mar-023.304-14.339-36.806-22.406-23.811-44.752
Apr-023.000-14.240-36.583-21.989-23.757-45.038
May-022.970-14.295-36.693-22.023-23.905-45.280
Jun-023.076-14.268-37.119-22.211-24.177-45.752
Jul-023.315-14.496-38.143-22.809-24.947-46.887
Aug-023.317-15.547-39.574-23.884-25.858-48.382
Sep-023.647-16.577-41.683-25.365-27.572-51.091
Oct-023.488-16.474-41.584-25.158-27.581-51.207
Nov-023.334-15.502-40.504-24.099-27.020-50.181
Dec-023.393-16.476-42.754-25.383-28.047-51.608
Jan-033.404-16.250-42.668-25.133-27.952-51.543
Feb-033.057-17.734-44.646-26.329-28.994-53.057
Mar-032.982-18.033-45.227-26.501-29.404-53.772
Apr-032.977-18.234-46.115-26.838-29.726-54.492
May-033.082-19.528-49.253-28.680-31.326-55.984
Jun-033.073-19.440-49.681-28.787-31.995-56.156
Jul-033.839-17.193-47.158-27.029-30.715-54.248
Aug-033.945-17.148-47.239-26.880-30.685-54.121
Sep-033.299-19.240-50.195-28.580-32.293-55.497
Oct-033.620-18.279-49.105-27.639-31.588-54.360
Nov-033.667-18.328-49.225-27.562-31.647-54.345
Dec-033.436-18.885-50.182-28.063-32.176-55.092

Figure 5a. Trace Cumulative Squared Prediction Errors, 3-Month Forecast Horizon, 1989 - 2003: Yield-Only Models

Data for Figure 5a immediately follows.

Data for Figure 5a

MonthARVARNS2-ARNS2-VARNS1ATSM
Jan-89#N/A#N/A#N/A#N/A#N/A#N/A
Feb-89#N/A#N/A#N/A#N/A#N/A#N/A
Mar-890.095-1.664-3.757-1.862-0.668-1.983
Apr-890.037-1.826-4.443-1.933-0.826-2.186
May-890.0502.095-0.2592.0573.0381.461
Jun-890.7435.4009.7517.04010.0564.093
Jul-890.4454.06514.3477.44014.2172.450
Aug-890.3522.09015.1006.18513.4470.475
Sep-890.7912.66815.9156.93014.1381.105
Oct-891.2302.33216.1706.92114.6090.755
Nov-890.537-0.01316.3115.56114.818-1.554
Dec-89-0.023-1.51616.8064.61315.123-2.973
Jan-900.7630.45318.3176.39416.466-1.046
Feb-902.0703.10219.8568.85918.9831.427
Mar-903.3675.54920.88510.98821.0513.704
Apr-904.1877.43821.74112.52121.0435.547
May-904.2727.35321.86912.54921.1035.433
Jun-903.9926.46821.99212.17421.7234.541
Jul-903.5496.98224.11213.41524.0424.933
Aug-903.4506.87524.30313.42423.9764.810
Sep-903.4696.80824.37413.28421.8404.771
Oct-903.4386.33923.64812.55921.0144.250
Nov-902.6261.70817.7317.67517.643-0.529
Dec-901.248-3.19410.2921.99912.631-5.334
Jan-91-0.337-7.9242.365-3.9584.878-10.097
Feb-91-1.843-10.923-2.246-7.738-2.460-12.992
Mar-91-2.861-12.366-4.897-9.320-5.785-14.448
Apr-91-4.164-14.935-9.488-12.106-8.834-17.041
May-91-5.164-16.501-12.484-13.705-11.187-18.655
Jun-91-5.660-17.325-14.358-14.459-11.731-19.684
Jul-91-5.783-17.830-15.887-14.912-12.163-20.378
Aug-91-7.332-20.833-21.982-17.843-15.656-23.279
Sep-91-10.238-25.675-32.331-22.654-21.243-27.587
Oct-91-13.802-32.868-46.765-30.326-30.804-34.109
Nov-91-17.995-41.865-64.182-39.809-43.211-42.233
Dec-91-23.878-53.684-85.813-51.905-59.500-53.150
Jan-92-27.632-61.364-102.994-60.231-67.312-59.996
Feb-92-29.427-65.042-114.202-64.176-68.734-63.088
Mar-92-26.483-59.542-108.067-58.647-63.122-58.546
Apr-92-26.709-59.840-112.795-58.666-67.574-58.937
May-92-28.199-62.716-121.735-61.090-71.063-61.296
Jun-92-31.916-68.547-136.223-65.895-77.242-65.918
Jul-92-36.910-75.650-156.799-72.097-85.811-71.043
Aug-92-42.020-84.514-178.898-79.884-97.161-77.647
Sep-92-48.142-95.914-206.354-90.130-111.680-86.185
Oct-92-49.397-98.442-215.106-91.773-115.064-87.674
Nov-92-47.985-96.072-215.913-89.246-113.971-85.511
Dec-92-45.725-92.556-214.894-85.848-110.520-82.558
Jan-93-47.842-96.295-226.910-88.560-115.156-84.746
Feb-93-52.589-102.594-244.131-93.014-122.359-88.538
Mar-93-56.117-107.820-258.670-96.579-128.325-91.599
Apr-93-58.520-112.797-271.543-100.075-133.139-94.562
May-93-58.358-113.508-275.973-100.161-134.141-94.499
Jun-93-59.697-116.908-285.128-102.284-137.602-96.319
Jul-93-60.281-119.166-292.775-103.576-139.674-97.398
Aug-93-63.289-124.839-305.108-107.347-144.967-100.815
Sep-93-65.269-129.031-312.952-109.771-148.887-103.176
Oct-93-67.048-132.502-319.399-111.627-150.151-105.020
Nov-93-66.149-131.655-319.096-110.628-149.605-104.011
Dec-93-65.225-130.751-318.433-109.691-149.108-103.093
Jan-94-65.533-131.845-320.245-110.076-150.215-103.483
Feb-94-64.301-130.256-318.943-108.670-149.182-102.180
Mar-94-60.399-124.646-311.056-104.744-145.465-98.516
Apr-94-53.526-114.501-297.245-98.178-138.257-92.126
May-94-48.682-108.923-288.739-94.708-134.468-88.704
Jun-94-45.929-106.837-284.316-93.661-133.966-87.738
Jul-94-45.367-106.492-283.802-93.521-133.812-87.655
Aug-94-44.934-106.030-283.285-93.176-133.429-87.403
Sep-94-43.533-105.689-282.011-93.268-133.241-87.550
Oct-94-41.037-104.614-279.419-93.011-132.801-87.276
Nov-94-37.776-102.318-275.620-91.705-131.296-85.914
Dec-94-35.912-101.847-274.249-91.872-131.097-85.937
Jan-95-34.929-100.605-273.129-90.870-129.481-84.951
Feb-95-35.724-98.739-271.043-88.742-127.285-83.041
Mar-95-36.328-94.896-266.479-84.624-123.800-79.161
Apr-95-37.360-94.559-265.065-83.878-122.796-78.722
May-95-39.320-96.410-265.576-84.955-123.443-80.232
Jun-95-41.659-99.557-267.028-87.165-124.173-82.945
Jul-95-43.398-102.627-268.887-89.519-125.684-85.576
Aug-95-43.914-104.335-269.687-90.785-127.294-86.868
Sep-95-44.226-105.563-270.181-91.580-128.056-87.783
Oct-95-45.514-108.956-272.836-94.241-129.884-90.676
Nov-95-47.136-112.904-275.332-97.126-131.893-93.980
Dec-95-49.560-117.824-277.753-100.863-135.146-97.958
Jan-96-51.772-122.605-280.171-104.445-139.026-101.788
Feb-96-51.891-123.052-279.916-104.622-139.779-101.765
Mar-96-49.813-119.351-277.502-101.627-136.856-98.584
Apr-96-46.744-112.044-271.245-95.535-131.766-92.205
May-96-44.671-108.078-267.543-92.207-129.503-88.793
Jun-96-44.155-107.206-266.641-91.466-129.160-87.972
Jul-96-43.813-106.898-266.340-91.190-129.044-87.719
Aug-96-43.713-106.906-266.234-91.145-129.153-87.768
Sep-96-43.919-107.217-266.301-91.286-129.357-87.993
Oct-96-45.242-108.599-267.013-92.064-129.556-89.043
Nov-96-47.266-110.461-268.261-92.954-128.990-90.442
Dec-96-48.090-111.398-268.832-93.452-129.102-91.185
Jan-97-47.987-111.412-268.663-93.355-129.131-91.146
Feb-97-46.846-109.698-267.391-91.985-128.077-89.671
Mar-97-45.557-108.197-266.305-90.894-127.430-88.485
Apr-97-44.921-107.463-265.652-90.328-127.213-87.888
May-97-44.927-107.580-265.562-90.444-127.440-87.983
Jun-97-45.965-108.581-265.790-90.858-127.117-88.791
Jul-97-47.465-109.706-265.946-91.190-126.862-89.504
Aug-97-48.134-110.037-265.854-91.158-126.881-89.681
Sep-97-49.224-111.404-266.315-91.919-126.894-90.690
Oct-97-49.922-112.793-266.673-92.746-127.419-91.744
Nov-97-50.923-114.140-267.048-93.402-127.481-92.825
Dec-97-51.571-114.781-267.132-93.477-127.272-93.255
Jan-98-52.657-116.777-267.602-94.572-128.049-94.784
Feb-98-53.494-118.151-267.619-95.208-128.418-95.797
Mar-98-53.973-119.315-267.653-95.773-128.951-96.603
Apr-98-53.783-119.217-267.208-95.605-129.104-96.308
May-98-54.292-120.371-267.185-96.391-129.870-97.104
Jun-98-54.987-122.025-267.376-97.279-130.187-98.331
Jul-98-55.477-122.802-267.434-97.640-130.599-98.862
Aug-98-57.332-124.767-266.726-98.460-132.129-100.084
Sep-98-61.152-130.616-265.981-101.886-134.674-104.386
Oct-98-64.868-135.430-264.822-104.599-137.109-107.766
Nov-98-66.470-138.899-265.519-106.794-139.438-110.188
Dec-98-65.857-138.183-265.346-106.093-138.961-109.473
Jan-99-65.477-138.176-265.017-105.661-138.625-109.196
Feb-99-63.919-135.358-263.628-103.602-136.885-106.911
Mar-99-62.717-133.326-262.876-102.240-135.792-105.258
Apr-99-61.190-130.521-261.847-100.461-134.715-103.040
May-99-60.667-130.063-261.692-100.260-135.049-102.764
Jun-99-59.338-128.001-260.484-98.882-134.634-101.135
Jul-99-57.911-126.057-259.461-97.714-134.190-99.751
Aug-99-57.037-125.331-259.555-97.535-134.274-99.333
Sep-99-56.908-125.385-259.607-97.621-134.469-99.418
Oct-99-56.624-125.184-259.703-97.629-134.663-99.359
Nov-99-56.080-124.718-259.969-97.485-134.452-99.080
Dec-99-54.529-123.362-260.159-96.916-134.287-98.214
Jan-00-52.648-122.159-261.188-96.545-133.325-97.594
Feb-00-51.608-121.324-261.761-96.028-132.619-97.055
Mar-00-51.429-120.897-261.766-95.369-131.714-96.751
Apr-00-51.678-121.025-261.756-95.247-131.453-96.882
May-00-52.021-121.579-261.857-95.835-132.026-97.388
Jun-00-52.234-121.890-262.128-96.028-132.146-97.590
Jul-00-52.492-121.042-262.237-94.990-131.042-96.800
Aug-00-52.645-117.412-260.623-91.102-126.962-93.283
Sep-00-53.160-117.499-260.419-90.940-126.592-93.334
Oct-00-53.811-118.840-260.322-91.833-127.051-94.511
Nov-00-54.783-121.321-260.042-93.535-128.566-96.750
Dec-00-56.540-125.534-260.128-96.887-132.357-100.472
Jan-01-58.956-131.741-259.862-102.146-138.895-105.595
Feb-01-61.369-138.351-260.471-107.624-145.650-110.875
Mar-01-63.653-143.667-261.732-111.803-151.226-114.634
Apr-01-64.950-145.114-262.787-112.737-153.113-115.302
May-01-66.103-145.214-263.083-112.539-149.309-114.633
Jun-01-66.525-144.476-262.681-111.647-148.616-113.645
Jul-01-68.313-147.699-266.845-113.852-151.067-116.039
Aug-01-70.399-151.335-272.034-116.166-153.026-118.651
Sep-01-75.380-158.499-281.898-121.108-158.138-123.789
Oct-01-81.130-169.250-297.402-129.036-166.165-131.764
Nov-01-85.359-175.284-306.165-132.884-171.306-135.973
Dec-01-86.308-175.659-308.602-132.479-171.630-136.193
Jan-02-85.052-171.330-304.524-128.666-167.660-133.075
Feb-02-85.143-171.846-306.787-128.640-167.619-133.517
Mar-02-83.952-170.294-304.909-127.473-166.330-133.062
Apr-02-84.351-171.306-307.527-127.785-166.602-134.058
May-02-84.637-172.066-309.704-127.903-166.690-134.680
Jun-02-87.403-174.536-315.878-128.283-166.955-135.690
Jul-02-90.321-178.863-325.775-130.160-168.619-137.665
Aug-02-93.707-184.017-337.382-132.600-170.827-139.890
Sep-02-97.912-192.431-354.632-137.452-175.574-144.146
Oct-02-100.739-200.849-371.296-143.246-182.841-149.078
Nov-02-102.009-203.567-377.863-144.375-185.356-150.192
Dec-02-103.094-206.518-384.056-145.516-187.847-151.033
Jan-03-103.884-209.051-390.819-146.508-189.897-151.815
Feb-03-106.038-215.093-402.668-149.859-194.345-154.643
Mar-03-106.734-218.212-409.574-151.289-196.623-155.790
Apr-03-107.815-222.184-417.995-153.333-199.532-157.521
May-03-109.227-227.938-428.058-156.433-203.956-160.105
Jun-03-110.857-233.434-438.841-159.311-208.116-162.539
Jul-03-110.513-232.254-439.712-157.778-207.010-161.156
Aug-03-108.854-225.622-433.298-153.034-201.959-156.684
Sep-03-108.473-225.244-434.490-152.277-201.565-155.886
Oct-03-109.001-227.252-441.329-153.211-202.989-156.639
Nov-03-109.618-228.987-447.294-153.893-204.244-157.276
Dec-03-109.189-228.222-448.592-152.864-203.456-156.386

Figure 5b. Trace Cumulative Squared Prediction Errors, 3-Month Forecast Horizon, 1989 - 2003: Macro Models

Data for Figure 5b immediately follows.

Notes: Figures 4 and 5 show the Trace Cumulative Squared Prediction Error [TCSPE], relative to the random walk, of individual yield-only models in Panel (a), and individual models with macro factors in Panel (b). Figure 4 shows TCSPEs for a 1-month forecast horizon whereas Figure 5 does so for a 3-month horizon. The forecast sample is 1989:1 - 2003:12.

Data for Figure 5b

MonthAR-XVAR-XNS2-AR-XNS2-VAR-XNS1-XATSM-X
Jan-89#N/A#N/A#N/A#N/A#N/A#N/A
Feb-89#N/A#N/A#N/A#N/A#N/A#N/A
Mar-891.338-1.287-7.793-5.722-1.962-3.324
Apr-891.458-1.521-10.077-7.085-2.669-3.580
May-891.3951.684-6.077-2.7101.9220.940
Jun-894.4406.8037.2208.17112.3017.694
Jul-896.1268.90214.87413.93819.1579.550
Aug-895.8399.17517.06115.60719.7759.355
Sep-895.4979.59917.36015.94820.13310.128
Oct-894.6209.92917.45516.00220.7749.829
Nov-895.11810.32819.73418.14722.2959.671
Dec-894.88810.87922.04920.39023.73610.561
Jan-904.77211.52120.34619.03124.02211.968
Feb-903.19910.89115.53814.49623.88511.106
Mar-901.8069.9809.5398.91422.6078.920
Apr-90-0.1819.2804.9104.86720.3927.948
May-90-0.5469.3433.8714.05119.9837.731
Jun-90-0.9169.5234.5634.85020.8957.918
Jul-900.14611.2309.6199.59825.25811.458
Aug-900.28311.6019.5539.80425.73911.985
Sep-90-0.02011.96110.21310.61426.23512.811
Oct-900.02012.32310.76811.23826.46413.154
Nov-902.11711.3918.7029.37425.67111.790
Dec-906.02510.7984.7746.52224.25510.244
Jan-918.5949.789-1.0522.52319.9698.541
Feb-9110.8049.952-3.4261.63015.9098.183
Mar-9111.54410.210-4.1481.84514.0638.699
Apr-9112.54810.200-5.7821.63013.0858.919
May-9112.78210.217-6.1471.86512.4479.345
Jun-9112.44410.234-5.9572.07812.3729.659
Jul-9111.99910.229-6.0471.69912.2229.287
Aug-9112.1159.335-7.3181.36211.3059.274
Sep-9113.0157.909-10.0430.6499.9689.837
Oct-9113.8725.609-15.305-2.1675.3298.592
Nov-9114.5812.857-22.283-6.118-1.6444.037
Dec-9118.6210.551-28.679-9.076-10.5261.897
Jan-9219.770-1.194-34.530-12.234-16.147-0.418
Feb-9219.936-1.664-37.622-13.719-19.030-1.178
Mar-9216.1970.916-31.779-9.657-14.2502.859
Apr-9214.0421.575-31.887-8.978-13.7623.752
May-9214.0101.114-34.313-10.088-15.1772.205
Jun-9214.349-0.865-40.476-13.596-17.8660.877
Jul-9216.790-3.608-53.285-21.317-23.015-3.432
Aug-9220.904-6.346-66.101-29.218-31.310-8.718
Sep-9224.494-10.702-83.527-40.163-43.212-16.482
Oct-9223.132-10.939-87.291-41.442-45.124-17.249
Nov-9220.271-9.097-85.523-38.928-42.948-14.892
Dec-9219.076-6.449-82.439-35.456-39.536-11.705
Jan-9319.898-7.693-87.850-37.739-43.011-13.262
Feb-9317.389-11.173-96.765-41.713-48.968-16.024
Mar-9317.037-13.558-104.192-45.029-54.465-18.402
Apr-9315.217-16.100-111.745-48.838-59.741-23.311
May-9314.502-15.841-112.916-48.757-60.326-23.518
Jun-9314.120-16.359-116.750-50.145-62.107-25.386
Jul-9312.141-16.513-119.043-50.715-63.016-26.553
Aug-9314.024-17.545-122.646-51.559-65.046-27.612
Sep-9314.469-18.173-124.033-51.592-65.972-28.923
Oct-9314.789-18.687-124.569-51.337-66.479-29.281
Nov-9313.952-18.213-124.283-52.182-66.118-29.770
Dec-9313.433-17.817-124.303-53.480-66.338-29.794
Jan-9413.082-17.755-124.423-54.165-66.701-30.014
Feb-9412.253-17.317-123.745-54.730-66.950-29.853
Mar-9410.435-16.423-122.185-56.415-67.632-30.646
Apr-9410.203-14.671-120.085-59.720-67.701-32.466
May-948.267-14.671-121.142-64.320-69.497-37.557
Jun-9410.168-13.943-121.306-66.836-71.192-39.750
Jul-9410.776-13.887-122.136-68.336-72.101-41.320
Aug-9410.417-14.128-123.382-69.969-72.955-43.658
Sep-9410.311-14.887-125.836-73.289-75.415-48.974
Oct-949.075-16.418-129.594-78.332-79.956-55.224
Nov-948.110-17.729-133.474-83.491-85.408-62.475
Dec-949.054-18.563-136.598-87.496-88.593-66.420
Jan-959.479-18.566-137.197-88.457-88.694-67.864
Feb-9510.395-16.409-133.701-84.763-84.901-64.121
Mar-9511.476-12.710-129.164-79.497-79.200-59.261
Apr-9513.123-10.871-126.057-76.217-75.762-55.937
May-9514.337-9.263-121.612-71.982-71.194-51.367
Jun-9516.613-7.628-116.381-67.154-65.544-45.828
Jul-9518.403-6.920-113.542-64.476-62.811-43.551
Aug-9518.372-6.805-113.626-64.466-62.652-43.666
Sep-9518.363-6.824-114.826-65.481-62.856-44.584
Oct-9518.755-6.946-114.430-65.117-62.033-44.514
Nov-9518.559-7.063-113.785-64.380-60.865-44.985
Dec-9518.532-6.593-110.601-61.406-58.493-42.232
Jan-9619.190-5.989-108.190-58.978-56.594-39.859
Feb-9618.683-5.549-108.840-59.335-56.604-39.923
Mar-9618.113-5.870-115.985-65.848-57.878-43.037
Apr-9617.399-4.875-119.260-69.542-59.436-43.365
May-9617.201-4.667-121.549-72.435-61.780-44.458
Jun-9616.968-4.670-124.031-74.753-63.867-45.893
Jul-9616.576-5.117-126.862-77.427-66.364-48.020
Aug-9616.667-5.292-128.950-79.263-68.260-49.419
Sep-9616.672-5.365-130.153-80.324-69.114-50.507
Oct-9617.235-4.612-128.540-78.671-67.349-49.051
Nov-9618.750-3.322-124.762-74.987-63.221-45.930
Dec-9619.201-2.981-124.448-74.578-62.728-45.678
Jan-9718.958-3.130-125.853-75.840-63.532-46.535
Feb-9718.867-3.390-129.579-79.013-65.010-47.802
Mar-9719.101-3.941-133.216-82.440-67.819-49.928
Apr-9718.732-4.340-135.201-84.384-69.899-51.506
May-9718.638-4.478-136.542-85.648-71.158-52.660
Jun-9718.862-4.034-135.251-84.347-69.764-51.728
Jul-9720.217-2.913-132.602-81.641-67.063-49.467
Aug-9720.685-2.441-132.882-81.552-66.503-49.526
Sep-9721.106-2.060-132.100-80.645-65.450-48.486
Oct-9721.306-1.936-133.084-81.133-65.522-48.804
Nov-9721.178-1.691-132.919-80.631-64.632-48.131
Dec-9721.384-1.441-134.112-81.083-64.324-48.243
Jan-9821.782-1.157-134.192-80.703-63.667-48.120
Feb-9821.773-0.934-134.918-80.725-63.305-48.148
Mar-9821.767-0.912-136.438-81.432-63.526-48.637
Apr-9821.493-0.920-138.907-82.931-64.151-49.329
May-9821.458-0.855-140.553-83.692-64.375-49.694
Jun-9821.670-0.803-141.833-84.173-64.514-49.933
Jul-9821.754-0.788-144.325-85.437-64.680-50.551
Aug-9821.8440.234-142.063-82.864-62.786-48.220
Sep-9825.4212.780-133.323-75.723-56.715-41.687
Oct-9830.0045.853-124.574-68.324-50.803-34.230
Nov-9830.7816.226-123.619-67.260-49.945-33.187
Dec-9830.4265.923-128.314-70.817-50.983-35.677
Jan-9930.0925.863-131.002-72.897-51.347-37.172
Feb-9930.3566.185-136.632-76.869-52.256-39.147
Mar-9929.9096.153-142.829-81.143-53.585-42.069
Apr-9929.7786.258-149.266-85.458-55.887-43.918
May-9929.4855.799-153.469-88.401-58.733-46.166
Jun-9928.2895.473-157.752-91.469-62.066-48.402
Jul-9927.8825.157-162.410-94.898-64.670-51.096
Aug-9926.8044.332-166.840-98.413-67.266-53.897
Sep-9926.8084.099-169.086-100.009-68.080-54.938
Oct-9927.1254.032-171.403-101.658-69.030-55.614
Nov-9927.1003.627-174.555-103.851-70.113-57.414
Dec-9925.7242.512-179.507-107.474-72.706-60.508
Jan-0025.2351.166-185.532-112.063-74.524-63.487
Feb-0024.5720.228-189.526-114.785-76.029-65.363
Mar-0024.7870.141-190.702-115.255-75.893-65.594
Apr-0024.8080.209-191.207-115.337-75.884-65.569
May-0024.7840.284-191.724-115.719-76.146-65.728
Jun-0024.7990.313-192.948-116.240-76.385-65.904
Jul-0024.8010.756-193.782-115.997-75.799-65.150
Aug-0025.5142.801-193.196-113.524-71.690-62.024
Sep-0025.6883.187-193.713-113.272-71.099-61.606
Oct-0025.9223.376-193.603-113.018-70.789-61.484
Nov-0026.5003.644-192.752-112.373-70.630-61.267
Dec-0026.9353.503-190.163-110.759-71.342-60.636
Jan-0124.9403.490-184.405-107.293-71.419-59.466
Feb-0127.2634.220-179.769-104.181-70.845-57.883
Mar-0130.5855.474-176.191-101.019-69.479-55.388
Apr-0131.7666.332-174.881-99.151-68.382-53.284
May-0132.5077.674-172.515-96.080-66.244-50.068
Jun-0132.5288.598-170.896-94.314-64.902-48.211
Jul-0132.3687.844-172.126-94.196-65.653-47.935
Aug-0132.0726.854-173.697-93.966-66.024-47.804
Sep-0132.9925.889-175.486-91.995-65.729-44.547
Oct-0132.4483.044-179.980-92.053-68.395-45.371
Nov-0129.6671.469-179.846-89.728-69.665-43.880
Dec-0129.5152.103-179.199-88.307-68.783-42.440
Jan-0231.1675.092-174.320-84.740-64.579-38.913
Feb-0230.9945.294-174.250-84.751-64.378-38.819
Mar-0230.2436.018-172.901-84.835-63.904-38.819
Apr-0230.1425.993-173.038-85.108-64.005-39.052
May-0230.1836.055-172.976-85.198-63.923-39.181
Jun-0228.5115.783-171.800-83.232-63.490-38.855
Jul-0228.3734.934-173.864-83.768-64.856-39.667
Aug-0229.4164.144-177.372-85.222-66.769-42.268
Sep-0230.2251.667-185.129-90.060-71.471-48.183
Oct-0230.493-1.280-194.432-96.629-77.519-54.245
Nov-0230.768-1.347-196.640-97.533-78.470-55.323
Dec-0230.813-1.444-198.711-98.349-79.281-55.963
Jan-0330.802-1.663-201.910-99.670-80.151-57.321
Feb-0331.435-3.440-209.945-103.884-83.555-60.589
Mar-0331.288-4.255-215.090-106.262-85.641-62.508
Apr-0329.875-5.972-222.397-110.020-89.423-66.243
May-0328.765-8.371-231.785-115.149-94.499-71.083
Jun-0328.762-10.297-243.043-120.792-99.100-75.421
Jul-0328.810-9.096-243.972-119.685-98.112-73.925
Aug-0328.944-5.095-237.249-114.340-92.662-69.037
Sep-0329.186-4.358-237.327-113.595-92.629-68.359
Oct-0328.309-5.358-242.984-115.992-94.935-70.187
Nov-0327.576-6.168-248.029-118.050-96.933-71.568
Dec-0328.014-5.255-248.706-117.341-96.708-70.736

Figure 6a. Trace Cumulative Squared Prediction Errors, 6-month Forecast Horizon, 1989 - 2003: Yield-Only Models

Data for Figure 6a immediately follows.

Data for Figure 6a

MonthARVARNS2-ARNS2-VARNS1ATSM
Jan-89#N/A#N/A#N/A#N/A#N/A#N/A
Feb-89#N/A#N/A#N/A#N/A#N/A#N/A
Mar-89#N/A#N/A#N/A#N/A#N/A#N/A
Apr-89#N/A#N/A#N/A#N/A#N/A#N/A
May-89#N/A#N/A#N/A#N/A#N/A#N/A
Jun-89-0.8133.6366.3294.3444.4143.422
Jul-89-1.9501.75511.8833.4175.4990.589
Aug-89-1.6298.95322.45010.71810.3877.503
Sep-89-0.35912.10532.97214.52716.0609.094
Oct-89-0.8729.84138.30213.47518.7445.761
Nov-89-1.5094.17740.7208.36213.796-0.915
Dec-89-2.047-0.61439.6944.19611.807-5.591
Jan-900.5194.02144.2218.88416.181-0.955
Feb-900.8303.93344.3159.20316.386-0.987
Mar-901.3404.51144.1749.90914.753-0.343
Apr-905.02713.55249.50817.91821.2858.364
May-907.59418.07951.71421.91225.19012.516
Jun-908.76619.72852.34123.48526.64514.045
Jul-907.98317.61451.94121.86322.36311.969
Aug-907.95317.02552.20321.48722.14011.269
Sep-907.65516.24553.11021.06822.51910.395
Oct-906.97816.69055.77621.98124.14010.480
Nov-905.47514.27055.80120.08522.0198.045
Dec-903.3518.66352.76714.6783.2742.520
Jan-910.6240.72645.3676.620-4.875-5.149
Feb-91-2.540-9.16831.054-4.261-14.509-15.462
Mar-91-6.122-17.63317.652-13.615-24.145-23.881
Apr-91-10.361-26.2562.815-23.854-38.912-32.115
May-91-14.145-32.741-5.484-30.789-52.057-37.792
Jun-91-16.655-36.456-10.776-34.127-58.677-40.839
Jul-91-19.115-41.256-18.223-38.391-63.816-44.843
Aug-91-23.615-48.460-29.006-44.373-71.639-50.651
Sep-91-30.091-59.459-45.417-52.662-77.789-59.794
Oct-91-37.382-70.759-64.062-61.351-85.944-68.764
Nov-91-47.313-85.812-89.718-73.674-101.446-80.537
Dec-91-61.128-104.968-125.734-89.397-120.995-95.371
Jan-92-72.964-123.832-160.717-106.408-143.271-110.670
Feb-92-83.204-142.476-194.199-122.901-165.556-125.542
Mar-92-89.547-153.888-213.905-132.019-179.481-134.027
Apr-92-96.492-166.647-240.117-142.543-189.840-143.069
May-92-102.466-178.523-267.050-151.438-192.973-150.455
Jun-92-105.403-187.083-285.439-155.686-200.637-154.336
Jul-92-116.045-207.136-328.610-169.529-236.444-166.580
Aug-92-128.497-229.461-373.291-184.550-256.833-180.043
Sep-92-145.692-255.516-424.676-201.060-278.639-195.780
Oct-92-157.170-272.678-464.171-210.917-293.098-204.635
Nov-92-164.366-285.514-493.606-218.200-304.923-211.410
Dec-92-171.920-300.305-527.825-227.006-319.169-219.134
Jan-93-178.410-315.105-558.290-234.100-331.349-225.382
Feb-93-185.909-333.475-598.297-244.155-333.108-233.567
Mar-93-189.189-345.417-628.571-248.763-342.364-236.940
Apr-93-197.647-361.946-664.057-256.323-355.581-243.213
May-93-206.248-375.983-693.542-262.219-366.004-248.575
Jun-93-215.233-391.710-726.346-268.677-377.806-254.240
Jul-93-220.822-405.077-753.602-273.938-386.235-258.828
Aug-93-226.616-421.132-781.828-280.503-397.803-264.480
Sep-93-232.993-437.806-810.202-287.263-409.222-270.582
Oct-93-237.596-452.260-837.220-293.110-418.596-275.620
Nov-93-241.614-463.273-854.993-296.993-425.248-279.214
Dec-93-243.535-471.692-865.086-298.907-430.135-281.110
Jan-94-247.503-483.241-877.712-302.437-432.306-284.745
Feb-94-243.163-479.247-872.956-297.595-427.969-279.962
Mar-94-233.222-463.370-856.621-287.473-417.574-269.828
Apr-94-219.872-440.475-834.200-273.889-403.277-256.145
May-94-207.251-420.111-812.145-261.177-389.984-243.606
Jun-94-193.357-397.823-787.602-248.206-376.088-230.801
Jul-94-178.906-374.416-763.864-235.036-361.283-217.486
Aug-94-168.741-360.565-749.008-227.200-352.428-209.514
Sep-94-160.215-351.101-736.785-222.801-348.515-204.897
Oct-94-153.926-345.798-729.700-221.261-345.591-203.058
Nov-94-146.339-339.219-722.329-218.978-341.605-200.421
Dec-94-139.351-333.928-715.718-217.676-339.026-198.755
Jan-95-132.203-326.108-707.825-213.387-333.693-194.256
Feb-95-128.876-321.824-704.095-210.279-329.673-191.019
Mar-95-127.592-318.705-702.051-207.417-326.232-188.134
Apr-95-128.019-316.093-700.974-204.240-322.910-185.057
May-95-132.100-312.935-694.091-198.293-316.174-180.273
Jun-95-136.447-306.199-678.123-188.335-308.051-171.696
Jul-95-140.932-308.957-674.500-188.356-307.177-172.783
Aug-95-145.463-315.692-676.100-192.251-310.844-177.411
Sep-95-150.306-323.930-679.102-197.430-314.089-183.469
Oct-95-155.568-334.310-684.102-204.504-319.545-191.213
Nov-95-159.686-347.316-690.237-213.430-328.840-200.682
Dec-95-165.017-361.353-696.286-222.728-337.900-210.510
Jan-96-171.425-377.435-706.451-233.879-347.456-222.312
Feb-96-174.782-386.164-710.010-239.310-352.604-228.099
Mar-96-175.864-390.094-710.435-241.217-354.908-230.194
Apr-96-174.644-388.776-708.179-239.555-354.653-228.324
May-96-170.560-380.245-701.322-232.150-348.770-220.462
Jun-96-165.415-371.034-695.985-225.316-342.453-213.162
Jul-96-158.720-357.593-685.273-214.324-332.326-201.916
Aug-96-154.527-350.528-679.162-208.473-327.614-195.926
Sep-96-153.975-350.611-678.309-207.872-327.356-195.375
Oct-96-156.103-354.403-680.083-209.523-328.446-197.462
Nov-96-160.039-359.996-682.809-211.890-328.836-200.682
Dec-96-162.038-363.281-683.946-213.298-330.020-202.465
Jan-97-164.361-367.026-685.169-215.116-331.343-204.707
Feb-97-166.497-370.246-686.433-216.529-331.918-206.645
Mar-97-165.716-369.780-685.690-215.916-331.684-206.101
Apr-97-164.196-368.111-683.928-214.281-330.493-204.418
May-97-161.983-365.010-681.457-211.722-328.659-201.592
Jun-97-162.013-365.974-681.248-211.790-328.974-201.855
Jul-97-164.113-370.530-683.134-213.897-330.179-204.511
Aug-97-165.500-373.382-683.785-215.092-330.949-206.096
Sep-97-169.299-378.457-685.052-217.370-331.202-209.189
Oct-97-173.301-383.894-686.048-219.654-332.355-212.219
Nov-97-176.359-387.621-686.352-220.698-333.276-213.964
Dec-97-179.547-393.189-687.931-223.059-333.663-217.193
Jan-98-182.912-401.386-689.953-227.304-336.645-222.294
Feb-98-186.298-407.738-691.394-230.180-337.970-226.093
Mar-98-188.454-412.052-691.803-231.592-338.814-228.193
Apr-98-190.207-416.958-692.235-233.825-340.960-230.870
May-98-192.788-422.988-692.339-236.783-343.564-234.379
Jun-98-195.036-429.427-692.778-239.874-346.417-238.082
Jul-98-195.654-433.309-692.751-241.300-347.948-239.653
Aug-98-200.248-445.053-694.172-247.629-353.018-246.947
Sep-98-208.800-464.468-696.559-258.382-359.451-259.592
Oct-98-216.950-479.502-696.120-265.611-366.228-268.270
Nov-98-223.305-491.177-694.666-270.583-372.700-274.388
Dec-98-229.575-504.896-694.143-277.226-378.120-282.405
Jan-99-236.055-517.694-693.117-283.087-383.362-289.490
Feb-99-236.126-519.925-692.166-283.204-384.210-289.671
Mar-99-232.441-513.819-690.792-278.746-380.034-284.856
Apr-99-228.583-507.885-687.010-273.710-375.362-279.723
May-99-224.387-500.009-683.414-268.040-370.491-273.603
Jun-99-219.227-490.207-680.976-262.042-365.289-266.768
Jul-99-213.141-477.815-677.592-254.738-360.115-258.239
Aug-99-210.274-473.736-676.772-252.402-359.454-255.372
Sep-99-207.426-469.630-674.390-249.445-358.003-252.001
Oct-99-204.035-464.581-672.116-246.240-356.001-248.364
Nov-99-201.174-461.049-671.773-244.381-354.857-245.976
Dec-99-197.767-456.849-671.263-242.263-353.035-243.328
Jan-00-193.333-451.585-670.659-239.879-352.267-240.184
Feb-00-190.025-447.835-670.995-237.988-350.232-237.854
Mar-00-186.536-443.578-670.838-235.192-347.953-234.806
Apr-00-183.579-440.447-672.034-233.610-345.927-232.873
May-00-182.549-439.913-673.188-233.647-346.077-232.671
Jun-00-182.705-440.220-673.409-233.231-345.346-232.517
Jul-00-183.600-440.706-672.906-232.339-343.574-232.359
Aug-00-185.035-442.420-672.380-232.197-342.589-233.087
Sep-00-186.437-444.788-672.166-232.843-342.346-234.289
Oct-00-188.046-444.807-670.726-231.047-339.676-233.272
Nov-00-190.046-440.652-664.768-224.455-334.131-227.722
Dec-00-194.164-446.462-659.973-226.303-334.718-230.950
Jan-01-199.710-458.735-654.522-234.177-340.963-239.608
Feb-01-205.552-473.645-649.946-243.974-350.472-250.557
Mar-01-212.166-489.198-646.908-254.985-364.448-261.741
Apr-01-217.541-502.770-643.376-265.186-378.103-271.455
May-01-222.579-514.824-639.853-274.015-391.063-279.300
Jun-01-226.575-522.988-638.061-279.004-399.672-283.485
Jul-01-232.074-535.134-644.251-286.176-408.668-290.561
Aug-01-237.997-549.039-652.024-294.424-405.991-298.517
Sep-01-248.028-569.594-666.757-306.299-417.695-310.295
Oct-01-261.874-595.130-690.572-320.869-434.736-325.098
Nov-01-273.613-615.483-710.473-331.293-445.247-336.514
Dec-01-284.363-633.269-727.452-340.778-455.805-346.623
Jan-02-292.766-648.533-744.703-348.511-464.919-354.559
Feb-02-300.787-663.629-759.730-355.529-474.385-361.939
Mar-02-300.041-661.842-758.577-351.736-471.082-359.106
Apr-02-298.318-659.209-756.997-346.876-466.276-355.081
May-02-299.027-664.050-763.883-347.071-466.620-355.840
Jun-02-302.619-674.149-779.160-349.511-469.235-358.906
Jul-02-309.181-689.089-800.384-353.806-474.260-363.428
Aug-02-316.487-706.325-824.070-358.983-480.407-368.607
Sep-02-329.323-723.857-849.965-360.136-481.060-370.375
Oct-02-340.224-745.721-881.262-366.624-486.777-377.056
Nov-02-349.247-765.005-906.939-372.823-492.689-383.607
Dec-02-359.522-790.050-942.028-382.072-502.320-392.597
Jan-03-366.515-812.805-977.139-391.843-515.991-401.235
Feb-03-373.230-836.385-1006.744-400.855-529.949-409.302
Mar-03-376.649-852.567-1024.136-404.722-536.850-412.581
Apr-03-380.295-870.043-1047.703-409.973-545.176-417.047
May-03-387.339-894.642-1079.805-418.262-556.864-424.327
Jun-03-391.967-915.750-1106.149-424.586-566.764-429.759
Jul-03-393.330-924.308-1118.735-425.280-568.910-430.356
Aug-03-392.577-925.642-1121.917-422.057-566.266-427.393
Sep-03-394.927-938.854-1140.058-424.739-571.135-429.635
Oct-03-395.262-944.626-1149.813-423.910-571.640-428.828
Nov-03-393.168-940.538-1146.265-418.205-565.871-423.311
Dec-03-391.567-940.613-1147.175-414.975-562.837-420.263

Figure 6b. Trace Cumulative Squared Prediction Errors, 6-Month Forecast Horizon, 1989 - 2003: Macro Models

Data for Figure 6b immediately follows.

Data for Figure 6b

MonthAR-XVAR-XNS2-AR-XNS2-VAR-XNS1-XATSM-X
Jan-89#N/A#N/A#N/A#N/A#N/A#N/A
Feb-89#N/A#N/A#N/A#N/A#N/A#N/A
Mar-89#N/A#N/A#N/A#N/A#N/A#N/A
Apr-89#N/A#N/A#N/A#N/A#N/A#N/A
May-89#N/A#N/A#N/A#N/A#N/A#N/A
Jun-89-1.0773.2828.1467.4946.4286.156
Jul-89-3.9515.18019.24515.04311.6776.885
Aug-89-4.22910.84531.27625.93119.44416.232
Sep-89-0.26414.84344.34036.58628.97122.771
Oct-891.15016.15753.11742.62535.06624.193
Nov-89-0.54316.75160.42247.26635.47023.015
Dec-890.06816.82761.39847.94535.56922.157
Jan-90-0.81519.03261.89948.99039.24025.999
Feb-90-1.03919.07155.32944.80838.47125.932
Mar-90-1.15818.87645.59838.46037.19425.196
Apr-90-1.08820.40834.18530.70238.37828.766
May-90-3.39620.09721.16420.15237.82626.717
Jun-90-4.70319.74110.20611.49936.56024.341
Jul-90-4.07720.0768.42910.79837.33724.717
Aug-90-4.28620.5116.2399.92537.63825.299
Sep-90-4.30721.2817.77712.23639.78127.161
Oct-90-1.62723.28915.11719.21045.47032.307
Nov-901.47224.59820.27424.24248.61235.735
Dec-901.01925.24427.92430.98950.03938.020
Jan-912.39524.91331.80434.41149.66737.571
Feb-919.91023.14731.57334.48349.66837.978
Mar-9117.97521.69528.46333.35149.00838.681
Apr-9124.30020.22221.46830.15942.92138.624
May-9128.15819.99620.19131.31337.53739.614
Jun-9128.69920.07820.30732.50935.38140.504
Jul-9128.82219.97519.81233.29834.89541.345
Aug-9130.79419.24919.58034.90833.86643.055
Sep-9130.99117.26219.96138.05534.18344.760
Oct-9133.21215.63120.82641.62834.60347.458
Nov-9135.47913.54120.00345.26132.46049.880
Dec-9141.45710.40016.41148.83130.30553.305
Jan-9245.1907.1799.26847.42822.33552.673
Feb-9246.9243.8930.31043.68311.94447.650
Mar-9247.8513.321-0.73444.6178.26747.888
Apr-9248.2702.520-4.96043.7693.48247.292
May-9248.5301.443-10.30041.756-1.55446.468
Jun-9245.8621.672-12.40241.779-2.49246.936
Jul-9250.528-2.265-26.83534.876-9.27543.322
Aug-9255.364-6.789-40.66828.319-18.36536.725
Sep-9259.924-12.869-61.27717.835-27.77331.924
Oct-9264.621-17.195-83.5216.394-35.68726.805
Nov-9266.423-19.572-96.9410.014-42.47223.439
Dec-9267.923-22.448-113.966-8.277-52.25418.525
Jan-9368.286-24.638-126.183-12.634-58.39716.225
Feb-9370.042-28.183-144.636-20.496-70.11212.174
Mar-9370.374-29.537-157.875-24.489-76.9719.957
Apr-9373.253-33.065-171.498-29.022-85.4307.594
May-9371.670-36.290-183.804-32.978-93.8774.100
Jun-9371.753-39.861-197.955-37.769-104.2820.575
Jul-9369.807-42.452-211.539-43.065-114.132-6.254
Aug-9371.394-44.803-223.223-47.163-122.671-10.547
Sep-9373.138-47.105-233.497-50.159-127.408-13.164
Oct-9373.069-48.822-240.886-51.992-130.868-14.945
Nov-9373.271-49.717-243.109-51.918-131.977-15.008
Dec-9372.673-49.675-243.136-52.296-132.138-15.067
Jan-9472.653-50.333-243.313-52.374-132.808-15.220
Feb-9469.636-48.014-243.662-57.079-131.317-16.406
Mar-9465.651-44.118-246.063-66.780-131.800-17.041
Apr-9460.681-39.689-251.213-79.806-133.059-20.229
May-9453.941-35.589-249.671-86.941-134.419-21.757
Jun-9447.224-31.349-247.994-95.388-136.119-25.128
Jul-9444.697-26.805-246.924-104.735-136.008-28.858
Aug-9441.265-24.911-250.471-115.248-139.059-36.488
Sep-9445.604-23.030-251.011-122.185-141.484-39.273
Oct-9448.616-23.146-257.104-132.104-147.171-45.127
Nov-9443.839-24.560-269.703-147.399-157.622-59.399
Dec-9442.252-25.707-279.208-160.383-166.900-73.959
Jan-9539.296-26.072-286.647-170.864-174.535-84.338
Feb-9538.792-25.855-289.969-175.642-178.182-88.954
Mar-9540.175-25.062-289.841-176.266-176.979-88.877
Apr-9541.589-23.654-286.796-173.234-172.797-85.721
May-9545.973-18.315-269.308-156.072-155.642-69.134
Jun-9551.466-9.278-244.112-130.912-132.216-44.553
Jul-9557.908-5.528-230.751-118.020-118.793-31.742
Aug-9561.052-3.989-223.731-111.211-111.725-25.026
Sep-9565.433-2.718-216.106-103.898-103.559-17.780
Oct-9569.878-1.936-208.935-97.099-96.487-12.155
Nov-9571.005-2.314-208.419-96.458-95.194-11.549
Dec-9571.887-2.475-205.317-93.394-92.443-9.200
Jan-9674.497-2.757-200.416-88.683-87.714-5.298
Feb-9674.506-2.647-200.187-88.000-86.283-4.533
Mar-9674.238-2.498-205.799-91.966-87.497-6.561
Apr-9672.553-2.232-215.724-99.519-90.736-11.599
May-9665.883-1.255-228.598-109.603-96.326-18.381
Jun-9664.256-1.049-249.635-127.635-100.507-26.108
Jul-9661.0430.507-262.457-140.007-104.846-30.965
Aug-9660.0021.246-270.099-148.125-109.180-34.152
Sep-9659.0661.191-277.386-154.402-113.620-37.345
Oct-9659.6391.416-279.376-155.917-114.135-37.920
Nov-9659.9332.154-275.986-152.378-109.912-35.287
Dec-9660.4062.406-277.253-153.218-109.943-35.607
Jan-9761.2042.802-277.557-153.032-109.389-35.062
Feb-9762.1233.121-277.794-152.873-108.952-34.834
Mar-9759.8432.638-284.839-159.202-114.636-39.611
Apr-9758.2762.463-291.739-165.264-118.353-43.071
May-9757.6952.490-301.145-172.736-121.492-45.712
Jun-9757.4762.314-305.453-176.476-123.803-47.542
Jul-9758.0642.317-305.971-176.762-123.411-47.763
Aug-9758.2602.374-307.749-178.142-124.257-48.464
Sep-9759.5943.201-303.345-173.843-119.609-45.075
Oct-9762.6714.376-299.041-169.344-114.760-41.223
Nov-9764.9075.388-298.054-167.591-111.878-39.301
Dec-9766.5305.838-297.502-166.294-109.499-37.195
Jan-9867.9166.061-299.013-166.500-108.429-37.002
Feb-9868.4526.449-298.720-165.223-106.000-35.142
Mar-9869.0886.738-302.595-167.115-105.851-35.527
Apr-9869.2336.767-307.370-169.789-107.009-36.830
May-9869.5637.002-310.213-170.733-106.826-36.827
Jun-9869.9717.097-313.844-172.240-106.955-37.233
Jul-9869.7547.120-320.488-176.000-108.169-38.773
Aug-9871.1387.437-319.004-173.447-105.267-36.279
Sep-9875.1138.159-305.960-162.876-95.479-28.982
Oct-9875.7899.340-293.839-152.216-88.175-22.481
Nov-9876.79110.688-287.101-145.227-83.207-16.886
Dec-9881.44311.907-280.807-138.808-76.961-11.008
Jan-9986.74513.419-273.682-131.527-70.105-3.926
Feb-9985.62113.758-281.499-136.219-71.706-6.350
Mar-9982.73514.296-300.060-150.041-76.753-14.762
Apr-9980.37015.377-313.138-160.051-79.767-20.418
May-9980.51816.609-329.486-170.795-82.058-24.072
Jun-9979.04517.377-352.071-185.922-87.543-31.936
Jul-9977.96818.624-374.480-200.318-95.115-36.692
Aug-9975.48518.201-389.880-210.787-104.608-43.144
Sep-9972.64818.448-400.831-218.269-111.984-47.570
Oct-9971.17918.563-412.800-226.613-117.857-52.519
Nov-9967.86117.972-425.387-236.134-124.930-58.871
Dec-9967.72317.470-437.494-244.779-129.520-63.261
Jan-0071.08117.242-449.445-253.209-133.979-65.481
Feb-0069.77916.326-461.026-261.299-138.535-70.696
Mar-0067.81715.884-471.260-268.229-143.344-75.803
Apr-0066.81415.060-481.449-275.591-146.506-79.926
May-0065.61114.308-488.508-280.522-149.684-83.166
Jun-0065.86314.299-491.084-281.777-149.850-83.616
Jul-0066.36814.760-491.648-281.090-148.610-82.513
Aug-0066.79615.114-491.611-280.090-147.144-81.280
Sep-0067.10815.579-493.388-280.116-146.605-80.838
Oct-0067.26216.856-493.239-278.071-143.894-78.183
Nov-0068.92920.407-488.680-270.838-136.218-70.312
Dec-0069.83221.773-481.564-264.392-131.957-66.220
Jan-0175.48323.595-468.257-254.537-124.249-58.983
Feb-0178.68124.142-454.358-244.927-119.888-53.516
Mar-0179.88924.884-437.821-232.897-118.445-46.851
Apr-0178.66126.051-421.352-221.189-115.325-41.294
May-0185.57628.284-404.646-207.750-108.199-31.914
Jun-0191.59430.505-393.123-197.177-101.278-23.005
Jul-0194.82130.419-390.286-193.120-99.380-19.235
Aug-0195.99729.920-387.994-189.106-98.751-16.717
Sep-0193.09127.779-388.752-185.153-99.562-14.908
Oct-0189.55224.019-391.465-180.081-103.583-12.455
Nov-0186.76521.312-392.593-174.984-104.384-10.271
Dec-0188.38519.914-391.652-169.473-102.840-5.469
Jan-0286.67918.435-391.144-165.300-103.199-3.599
Feb-0282.64917.139-389.412-161.224-104.810-2.420
Mar-0284.06319.806-383.979-157.298-100.0551.657
Apr-0286.96223.574-377.728-152.085-94.1407.075
May-0287.14524.035-377.301-151.841-93.5467.611
Jun-0287.17122.965-379.868-152.183-94.5087.105
Jul-0287.46121.064-382.226-151.552-96.0096.720
Aug-0285.62418.358-385.428-152.203-99.7204.371
Sep-0278.83316.331-382.904-146.425-100.2823.836
Oct-0277.39012.542-391.214-150.520-105.528-2.052
Nov-0278.5239.522-399.490-155.207-109.365-8.068
Dec-0278.0664.339-415.282-165.678-118.257-18.673
Jan-0377.768-0.095-433.688-178.232-129.498-28.184
Feb-0379.261-4.094-448.155-187.967-138.831-36.000
Mar-0379.372-5.320-454.492-191.393-141.625-38.062
Apr-0379.430-7.514-466.550-197.991-146.435-42.641
May-0380.417-12.541-487.250-208.862-155.099-49.392
Jun-0378.324-16.490-506.944-219.343-165.074-57.236
Jul-0376.345-16.681-517.053-223.117-169.650-60.657
Aug-0377.376-13.950-518.786-220.991-167.733-58.217
Sep-0376.963-15.432-536.557-228.487-173.581-62.230
Oct-0377.310-14.472-545.531-230.148-174.744-61.922
Nov-0379.215-9.757-539.201-223.903-168.562-55.775
Dec-0380.497-6.675-537.117-220.435-166.310-52.342

Figure 7a. Trace Cumulative Squared Prediction Errors, 12-Month Forecast Horizon, 1989 - 2003: Yield-Only Models

Data for Figure 7a immediately follows.

Data for Figure 7a

MonthARVARNS2-ARNS2-VARNS1ATSM
Jan-89#N/A#N/A#N/A#N/A#N/A#N/A
Feb-89#N/A#N/A#N/A#N/A#N/A#N/A
Mar-89#N/A#N/A#N/A#N/A#N/A#N/A
Apr-89#N/A#N/A#N/A#N/A#N/A#N/A
May-89#N/A#N/A#N/A#N/A#N/A#N/A
Jun-89#N/A#N/A#N/A#N/A#N/A#N/A
Jul-89#N/A#N/A#N/A#N/A#N/A#N/A
Aug-89#N/A#N/A#N/A#N/A#N/A#N/A
Sep-89#N/A#N/A#N/A#N/A#N/A#N/A
Oct-89#N/A#N/A#N/A#N/A#N/A#N/A
Nov-89#N/A#N/A#N/A#N/A#N/A#N/A
Dec-89-1.8792.4127.7902.3350.4941.297
Jan-90-2.7001.23411.0770.089-1.691-1.959
Feb-90-1.8907.32020.5625.5290.6342.875
Mar-900.43811.99530.2537.8843.7863.298
Apr-901.19712.85331.6768.0033.9272.951
May-901.83811.74234.3255.623-0.183-0.174
Jun-902.6659.67835.4473.977-1.046-2.210
Jul-904.7188.52537.6453.671-1.960-2.475
Aug-905.4488.96339.3534.294-1.808-2.323
Sep-905.7258.98041.8444.159-9.341-2.762
Oct-906.8608.72744.7524.180-10.626-2.775
Nov-905.9574.94345.6111.957-15.374-5.047
Dec-902.303-2.84746.271-3.606-24.797-10.850
Jan-91-2.340-11.48845.769-11.476-63.230-19.385
Feb-91-6.572-19.90544.550-19.914-71.956-29.005
Mar-91-10.027-25.49047.391-25.498-77.673-36.391
Apr-91-12.647-24.97953.557-25.934-78.967-38.837
May-91-17.638-31.77554.165-32.176-88.477-46.169
Jun-91-22.099-40.03351.359-40.623-135.038-54.805
Jul-91-28.138-52.36441.840-52.724-150.211-66.356
Aug-91-36.703-68.38417.162-70.844-169.618-83.721
Sep-91-48.247-87.510-12.163-90.813-192.635-102.310
Oct-91-62.219-110.874-45.791-114.221-225.719-122.847
Nov-91-79.510-139.834-73.099-139.086-265.721-145.359
Dec-91-105.421-181.437-114.119-168.835-309.388-173.551
Jan-92-128.094-220.995-156.031-197.432-343.343-201.229
Feb-92-150.359-257.248-193.486-220.595-373.987-224.243
Mar-92-169.641-289.561-228.653-240.038-393.778-245.100
Apr-92-191.529-325.775-268.896-261.019-417.691-266.976
May-92-215.410-364.708-316.151-284.188-447.918-290.252
Jun-92-241.896-405.034-370.839-308.169-478.806-314.250
Jul-92-273.823-456.219-442.756-341.901-523.389-346.347
Aug-92-307.978-517.700-523.063-382.060-576.769-384.125
Sep-92-346.996-591.240-605.412-426.711-637.419-426.407
Oct-92-377.739-653.293-684.568-463.790-675.463-460.081
Nov-92-400.206-703.326-749.059-487.478-682.026-481.547
Dec-92-419.144-757.164-804.048-506.564-709.528-499.978
Jan-93-447.914-821.296-887.796-532.579-793.024-524.383
Feb-93-481.028-890.701-976.243-560.887-832.321-551.348
Mar-93-515.022-954.376-1059.880-585.258-865.393-575.906
Apr-93-547.823-1017.284-1148.102-605.334-895.362-595.015
May-93-575.185-1076.642-1226.560-625.786-927.217-614.327
Jun-93-604.055-1144.162-1316.352-649.938-965.294-635.919
Jul-93-625.444-1207.827-1385.341-665.958-992.827-650.809
Aug-93-648.860-1279.924-1470.409-686.141-996.339-668.431
Sep-93-666.627-1349.103-1547.692-699.310-1022.742-679.494
Oct-93-689.436-1412.512-1618.832-711.914-1046.663-690.884
Nov-93-711.378-1466.765-1677.534-723.329-1066.871-702.242
Dec-93-730.716-1521.633-1733.474-733.725-1085.970-712.664
Jan-94-748.068-1581.599-1790.454-745.366-1104.899-723.836
Feb-94-749.986-1614.877-1814.564-745.490-1110.067-723.861
Mar-94-742.284-1625.291-1816.603-737.126-1101.243-715.949
Apr-94-724.277-1612.690-1799.118-718.173-1080.634-697.734
May-94-706.476-1597.565-1778.955-701.125-1061.680-680.997
Jun-94-681.379-1567.192-1744.481-676.624-1033.524-656.526
Jul-94-659.710-1544.787-1717.142-656.474-1016.696-636.187
Aug-94-629.272-1502.841-1675.581-625.321-981.847-604.796
Sep-94-590.460-1438.773-1621.512-587.067-939.237-565.707
Oct-94-549.563-1367.947-1564.752-546.620-894.597-524.307
Nov-94-506.164-1292.876-1501.001-505.281-848.096-482.544
Dec-94-461.425-1214.466-1435.353-463.938-801.336-440.440
Jan-95-415.721-1134.499-1372.424-421.384-752.536-396.781
Feb-95-388.566-1095.255-1338.757-397.627-725.461-372.124
Mar-95-370.068-1070.662-1316.668-382.484-709.137-356.277
Apr-95-360.532-1059.214-1306.214-372.830-697.126-346.148
May-95-361.211-1061.760-1305.826-366.555-690.974-340.096
Jun-95-364.394-1065.627-1307.514-360.115-684.854-333.962
Jul-95-365.807-1070.907-1308.993-356.693-681.463-330.921
Aug-95-370.635-1081.764-1314.778-356.973-683.535-331.831
Sep-95-378.090-1090.686-1320.891-355.201-682.503-330.858
Oct-95-387.707-1100.135-1327.570-353.286-682.539-329.926
Nov-95-399.231-1110.593-1320.775-351.260-679.342-330.667
Dec-95-412.498-1121.377-1297.999-347.093-678.116-330.046
Jan-96-427.723-1145.104-1294.731-356.622-686.838-342.464
Feb-96-440.338-1171.497-1300.728-370.389-701.706-357.873
Mar-96-450.363-1193.832-1306.910-382.477-712.947-371.348
Apr-96-457.973-1212.899-1312.525-392.897-724.078-382.439
May-96-458.146-1222.098-1310.776-394.865-729.086-384.607
Jun-96-458.844-1232.852-1309.738-397.395-733.646-387.316
Jul-96-459.727-1242.618-1310.415-399.902-737.359-390.091
Aug-96-458.088-1247.040-1307.483-398.710-737.602-389.065
Sep-96-458.607-1257.015-1306.079-400.667-741.306-391.322
Oct-96-460.918-1273.470-1306.447-405.649-748.786-396.825
Nov-96-463.308-1294.680-1307.657-412.579-758.032-404.237
Dec-96-458.779-1298.239-1302.429-407.827-755.696-399.590
Jan-97-452.590-1298.503-1294.460-400.477-749.910-392.291
Feb-97-450.300-1303.778-1291.933-398.561-748.788-390.540
Mar-97-447.499-1305.007-1288.553-395.685-746.640-387.827
Apr-97-448.582-1312.107-1288.983-396.785-748.148-389.295
May-97-452.310-1322.614-1291.337-400.066-751.072-393.213
Jun-97-455.848-1333.897-1293.229-403.274-754.554-397.085
Jul-97-463.515-1352.746-1297.999-410.522-760.786-405.495
Aug-97-469.627-1367.052-1302.010-415.785-764.890-411.738
Sep-97-476.365-1384.521-1306.769-422.246-770.600-419.144
Oct-97-482.535-1405.549-1312.218-430.210-778.997-427.999
Nov-97-485.635-1422.948-1314.152-435.292-784.802-433.883
Dec-97-492.084-1443.315-1318.758-442.479-791.689-442.243
Jan-98-501.748-1469.806-1326.686-453.270-800.815-454.476
Feb-98-510.359-1492.722-1331.990-462.094-807.749-464.908
Mar-98-520.270-1513.579-1336.776-470.104-812.225-474.796
Apr-98-530.140-1535.673-1340.839-478.849-819.734-484.958
May-98-539.970-1557.722-1344.270-486.736-828.011-494.390
Jun-98-549.491-1582.225-1349.538-496.379-834.451-505.644
Jul-98-556.598-1607.756-1353.173-506.486-843.527-517.082
Aug-98-570.461-1642.847-1359.937-521.544-855.733-534.383
Sep-98-590.163-1692.137-1366.936-542.195-874.792-557.881
Oct-98-608.511-1744.030-1373.806-565.600-897.565-583.844
Nov-98-624.541-1789.966-1376.315-585.520-915.760-606.513
Dec-98-640.001-1837.983-1380.354-607.276-937.163-630.695
Jan-99-653.852-1886.796-1386.564-628.729-958.698-653.499
Feb-99-662.030-1917.483-1388.036-640.947-970.682-667.120
Mar-99-671.605-1950.233-1389.993-654.252-981.685-682.203
Apr-99-680.183-1978.324-1390.383-663.936-992.002-693.382
May-99-684.643-1996.955-1389.830-669.069-999.551-699.393
Jun-99-687.111-2012.166-1388.907-672.531-1003.785-703.509
Jul-99-688.558-2023.713-1387.976-674.467-1007.086-705.948
Aug-99-682.510-2021.383-1382.998-666.778-1001.009-698.050
Sep-99-669.310-2004.289-1379.026-650.837-985.446-681.312
Oct-99-654.535-1983.597-1367.589-632.624-967.348-662.584
Nov-99-640.216-1962.453-1359.416-614.809-950.066-643.996
Dec-99-622.589-1931.825-1352.972-593.890-929.959-621.672
Jan-00-600.679-1890.413-1344.815-567.882-906.795-593.790
Feb-00-587.933-1872.163-1341.100-555.182-896.849-580.133
Mar-00-575.001-1856.222-1333.919-542.130-885.794-566.532
Apr-00-561.918-1838.551-1327.038-529.240-874.286-552.839
May-00-554.116-1830.044-1324.762-522.915-869.109-545.663
Jun-00-548.193-1825.766-1323.153-517.663-863.506-540.027
Jul-00-542.275-1820.958-1321.053-511.892-857.820-533.957
Aug-00-539.476-1821.532-1320.600-508.359-853.403-530.544
Sep-00-536.521-1822.296-1319.915-504.813-849.136-527.126
Oct-00-534.808-1824.140-1319.675-501.544-844.943-524.048
Nov-00-538.107-1835.229-1320.262-503.320-845.723-526.752
Dec-00-546.301-1853.474-1320.410-509.120-849.939-534.132
Jan-01-558.590-1876.568-1314.453-517.611-852.982-545.403
Feb-01-571.886-1903.924-1307.817-528.827-860.277-559.642
Mar-01-586.187-1938.003-1294.799-544.333-870.851-578.238
Apr-01-599.644-1963.892-1275.499-553.261-875.865-590.895
May-01-614.007-1985.835-1250.863-556.991-886.118-598.380
Jun-01-627.168-2015.167-1235.451-570.260-899.389-614.343
Jul-01-641.909-2054.027-1221.979-592.305-920.432-638.208
Aug-01-657.594-2098.813-1208.398-618.135-947.913-666.020
Sep-01-678.638-2153.737-1197.617-651.125-989.676-699.815
Oct-01-701.949-2219.653-1188.390-693.255-1041.257-742.464
Nov-01-722.253-2276.752-1178.641-727.543-1086.217-776.270
Dec-01-741.057-2327.095-1174.870-753.434-1122.558-801.564
Jan-02-762.016-2378.621-1188.444-775.747-1152.054-823.786
Feb-02-783.047-2433.865-1204.448-799.421-1141.032-846.997
Mar-02-797.693-2470.480-1214.914-810.664-1155.044-858.361
Apr-02-819.066-2521.706-1241.689-829.588-1178.634-878.110
May-02-840.826-2575.046-1272.093-847.885-1198.345-897.769
Jun-02-865.708-2634.357-1306.254-869.289-1222.301-920.107
Jul-02-892.191-2707.438-1354.063-896.995-1253.941-947.733
Aug-02-919.662-2787.260-1400.333-924.531-1288.237-975.322
Sep-02-945.772-2883.209-1464.910-950.898-1323.355-1000.513
Oct-02-965.016-2973.546-1521.368-970.399-1349.703-1019.294
Nov-02-984.359-3050.667-1573.070-985.033-1366.479-1034.542
Dec-02-1010.701-3139.345-1642.111-1001.757-1384.680-1052.253
Jan-03-1035.927-3222.654-1702.463-1017.782-1402.683-1069.373
Feb-03-1062.124-3312.589-1765.549-1035.267-1422.567-1087.627
Mar-03-1092.330-3392.436-1819.805-1047.311-1433.059-1101.941
Apr-03-1119.393-3477.923-1882.953-1063.710-1448.417-1119.746
May-03-1149.101-3572.689-1951.795-1082.023-1466.576-1138.764
Jun-03-1176.992-3671.491-2026.239-1102.993-1489.245-1159.985
Jul-03-1192.455-3747.111-2085.692-1117.696-1510.844-1173.963
Aug-03-1203.138-3812.458-2122.763-1126.290-1525.437-1182.489
Sep-03-1213.902-3894.167-2159.903-1135.894-1541.761-1191.289
Oct-03-1221.111-3959.284-2196.751-1141.236-1552.586-1196.072
Nov-03-1229.848-4022.315-2232.290-1147.748-1562.557-1202.632
Dec-03-1235.003-4084.225-2262.749-1150.807-1569.708-1205.495

Figure 7b. Trace Cumulative Squared Prediction Errors, 12-Month Forecast Horizon, 1989 - 2003: Macro Models

Data for Figure 7b immediately follows.

Notes: Figures 6 and 7 show the Trace Cumulative Squared Prediction Error [TCSPE], relative to the random walk, of individual yield-only models in Panel (a), and individual models with macro factors in Panel (b). Figure 6 shows TCSPEs for a 6-month forecast horizon whereas Figure 7 does so for a 12-month horizon. The forecast sample is 1989:1 - 2003:12.

Data for Figure 7b

MonthAR-XVAR-XNS2-AR-XNS2-VAR-XNS1-XATSM-X
Jan-89#N/A#N/A#N/A#N/A#N/A#N/A
Feb-89#N/A#N/A#N/A#N/A#N/A#N/A
Mar-89#N/A#N/A#N/A#N/A#N/A#N/A
Apr-89#N/A#N/A#N/A#N/A#N/A#N/A
May-89#N/A#N/A#N/A#N/A#N/A#N/A
Jun-89#N/A#N/A#N/A#N/A#N/A#N/A
Jul-89#N/A#N/A#N/A#N/A#N/A#N/A
Aug-89#N/A#N/A#N/A#N/A#N/A#N/A
Sep-89#N/A#N/A#N/A#N/A#N/A#N/A
Oct-89#N/A#N/A#N/A#N/A#N/A#N/A
Nov-89#N/A#N/A#N/A#N/A#N/A#N/A
Dec-89-2.8023.55512.46610.3474.8016.504
Jan-90-5.1884.56017.18714.3055.9446.607
Feb-90-5.6549.61726.72023.93711.79214.440
Mar-90-2.29113.25236.23633.59519.58420.854
Apr-90-1.71213.88635.30134.76720.71922.148
May-90-2.22014.81936.87037.54721.24922.760
Jun-90-1.66715.73634.11836.85722.48523.801
Jul-90-1.25517.47130.20935.48225.07225.966
Aug-90-1.66618.29516.48829.39526.54928.039
Sep-90-2.13119.3914.82825.83229.06431.147
Oct-90-2.28321.011-5.75422.19632.29234.860
Nov-90-2.64221.724-18.89414.85933.71135.884
Dec-90-1.25923.069-19.41917.91137.23340.554
Jan-914.67825.081-6.60231.23545.27249.168
Feb-9112.85827.09312.18648.95156.16160.917
Mar-9115.29429.19535.03269.32967.71969.489
Apr-9124.99933.79667.19797.38185.46386.953
May-9134.42137.13890.683118.74696.64599.862
Jun-9135.80838.435107.726134.252100.863106.494
Jul-9138.55338.402119.241144.239102.339109.540
Aug-9151.38635.755128.266151.768105.916115.480
Sep-9167.82032.820131.846157.512108.769122.403
Oct-9178.87629.122126.622158.38099.698125.656
Nov-9187.65227.281130.715167.64687.161129.206
Dec-9195.32124.596134.282180.13473.143133.884
Jan-92108.41421.573139.286192.98772.588140.023
Feb-92117.08819.746148.326207.55672.053147.098
Mar-92118.62017.271156.783219.11873.117150.018
Apr-92123.35915.019165.864231.14875.287154.708
May-92129.09611.488171.017241.09973.673157.575
Jun-92138.4647.097171.979248.75572.475160.180
Jul-92147.7130.055163.783248.87459.476156.672
Aug-92152.984-9.299145.964240.33235.675142.561
Sep-92163.310-17.913137.435238.73214.170133.608
Oct-92168.028-25.711120.572229.657-5.220122.685
Nov-92170.449-30.480108.278224.009-16.895118.112
Dec-92169.396-33.62998.941221.374-22.961115.420
Jan-93177.712-41.56175.535210.922-32.565110.279
Feb-93187.401-51.06653.232201.587-45.907100.862
Mar-93194.139-61.13923.303187.016-57.73893.073
Apr-93204.137-71.544-22.774165.282-70.37085.844
May-93212.468-79.691-56.301149.899-85.36278.990
Jun-93219.914-89.419-96.585131.375-107.38668.831
Jul-93224.758-94.939-118.010126.150-116.48466.600
Aug-93230.749-102.554-148.222116.517-134.98761.862
Sep-93234.219-108.115-176.320109.821-151.29557.667
Oct-93241.072-114.270-194.788108.132-161.74557.128
Nov-93239.742-120.225-214.670103.779-176.50650.639
Dec-93239.944-125.216-234.13198.942-191.44645.205
Jan-94235.519-130.499-260.66389.254-213.51931.118
Feb-94234.654-128.293-262.76591.645-213.81333.295
Mar-94223.749-122.148-253.98296.281-206.80537.472
Apr-94202.708-111.683-237.185101.371-194.49041.706
May-94189.098-103.280-229.98294.256-188.34039.859
Jun-94179.854-91.679-227.17478.800-180.50742.904
Jul-94174.935-82.417-232.39958.015-175.63441.771
Aug-94162.783-69.587-246.27927.451-170.92034.719
Sep-94150.502-54.272-266.531-12.583-172.40328.692
Oct-94136.324-39.200-293.171-57.144-176.59217.222
Nov-94118.355-24.510-303.020-90.646-182.4286.469
Dec-94102.193-9.693-311.797-125.904-187.788-6.653
Jan-9596.1876.056-320.829-161.605-186.958-18.230
Feb-9589.93613.089-335.409-192.187-192.606-32.964
Mar-9598.67018.681-335.638-204.428-189.309-31.786
Apr-95104.88821.555-339.744-214.426-188.446-32.425
May-95108.50623.699-338.944-215.179-183.685-30.750
Jun-95114.03226.286-332.129-209.429-174.213-23.648
Jul-95116.27527.586-332.129-211.586-171.783-24.101
Aug-95119.23428.242-329.972-210.268-167.470-21.514
Sep-95123.32830.017-320.282-199.708-155.758-10.731
Oct-95129.35332.533-305.626-182.684-139.1095.865
Nov-95140.16039.211-272.642-150.316-107.31135.580
Dec-95154.52950.943-224.099-102.659-63.27779.498
Jan-96174.27257.311-185.018-65.293-25.818114.515
Feb-96182.97359.158-170.707-50.820-11.001128.762
Mar-96190.28260.286-164.228-43.733-1.811136.798
Apr-96194.00460.932-167.080-45.1181.225138.991
May-96191.70162.107-186.107-60.556-1.099132.760
Jun-96189.79962.889-208.734-79.323-5.058126.220
Jul-96186.79063.371-227.762-96.528-11.396117.284
Aug-96184.33564.106-252.193-116.816-18.730108.754
Sep-96182.13864.666-277.795-136.294-24.866100.571
Oct-96179.66265.093-301.990-154.456-30.12591.880
Nov-96173.99065.728-327.619-173.876-37.78080.890
Dec-96170.04466.989-370.691-208.767-44.23868.467
Jan-97163.40169.447-400.731-235.558-51.67557.586
Feb-97161.07870.355-416.652-250.876-56.77951.965
Mar-97156.11870.716-442.849-273.086-69.12141.458
Apr-97152.53870.550-460.502-288.834-79.58732.805
May-97152.72370.576-468.821-295.601-83.04830.373
Jun-97152.44970.558-477.755-303.124-86.80826.439
Jul-97155.22070.791-478.507-302.851-84.43527.893
Aug-97157.17970.982-481.165-304.494-84.23627.721
Sep-97158.82771.056-484.704-307.232-84.55327.046
Oct-97159.65670.686-490.670-312.037-85.30824.792
Nov-97159.52570.491-504.492-322.501-87.85321.265
Dec-97160.78670.136-508.616-325.758-87.41820.275
Jan-98163.80669.584-506.888-323.732-83.52922.120
Feb-98166.52369.422-506.066-322.366-79.91424.247
Mar-98170.84369.905-498.747-314.870-71.01630.699
Apr-98176.47770.664-495.059-310.382-64.52935.531
May-98182.07171.620-494.070-307.964-58.90339.519
Jun-98186.41671.696-495.190-307.255-54.51543.248
Jul-98187.74171.443-508.467-315.628-56.71540.193
Aug-98192.28871.437-500.109-306.686-46.72548.237
Sep-98200.05471.727-481.129-288.740-30.85763.022
Oct-98208.64471.325-467.187-275.085-17.99473.566
Nov-98213.64671.229-456.644-264.007-6.96282.114
Dec-98219.25970.723-448.317-254.7622.42390.417
Jan-99222.42969.330-445.634-250.2557.10393.531
Feb-99223.76769.203-456.073-253.6408.32694.574
Mar-99226.13068.970-461.426-253.47210.98997.365
Apr-99226.82068.937-470.145-255.75912.91998.950
May-99226.21669.130-489.514-265.46111.28796.858
Jun-99222.08669.525-515.422-279.9801.37488.316
Jul-99216.60769.828-544.983-297.733-9.81777.480
Aug-99209.48371.913-581.914-321.948-20.02265.994
Sep-99198.64675.909-641.930-366.728-38.82741.319
Oct-99189.02180.641-689.000-402.918-51.39223.298
Nov-99186.88885.090-741.309-437.824-59.17113.814
Dec-99179.95489.541-807.940-482.104-74.967-4.480
Jan-00173.52095.327-876.697-526.454-96.344-19.301
Feb-00162.98796.420-925.432-560.286-124.415-39.531
Mar-00152.97098.202-963.973-587.796-147.694-55.514
Apr-00147.262100.024-1000.857-614.109-164.231-69.315
May-00139.352100.127-1031.226-637.342-181.222-84.015
Jun-00138.886100.442-1052.904-652.513-188.015-90.590
Jul-00143.498101.355-1067.611-662.054-189.885-90.753
Aug-00143.089101.555-1081.801-671.231-193.942-95.885
Sep-00141.996101.828-1094.709-679.516-198.853-101.187
Oct-00142.239102.210-1105.589-686.251-200.287-103.106
Nov-00143.169102.377-1109.655-687.740-199.585-102.816
Dec-00145.837102.777-1102.792-681.296-193.179-97.541
Jan-01149.304104.202-1083.347-665.477-178.163-86.002
Feb-01151.337105.269-1063.006-649.779-166.722-77.315
Mar-01158.517107.185-1035.575-628.441-150.440-64.863
Apr-01160.151110.624-1006.926-605.025-133.681-51.103
May-01163.084116.185-972.745-574.830-118.104-30.705
Jun-01166.579118.515-942.724-550.218-105.024-16.484
Jul-01181.415120.907-904.857-519.666-82.1557.066
Aug-01191.155122.416-863.898-488.466-65.92125.243
Sep-01198.996123.746-807.283-444.857-54.05546.945
Oct-01202.045123.689-747.783-403.502-43.66162.924
Nov-01223.459125.891-690.642-358.545-18.91092.298
Dec-01243.426128.450-646.704-320.6015.023121.032
Jan-02254.237128.211-624.961-298.17817.773138.494
Feb-02258.705127.080-605.847-277.83724.586150.080
Mar-02258.302127.399-593.894-264.77430.068158.478
Apr-02255.159124.305-588.131-254.73328.090161.224
May-02251.942120.585-584.740-246.24326.756162.510
Jun-02254.317116.681-579.660-235.24829.200168.586
Jul-02248.095110.034-582.049-230.77018.728162.130
Aug-02237.490102.561-583.199-226.6163.311153.297
Sep-02227.72192.235-607.214-235.290-19.515139.213
Oct-02206.85383.305-634.691-249.111-56.058112.038
Nov-02202.16276.533-648.170-253.149-68.506102.645
Dec-02199.43167.413-668.530-259.831-79.05994.242
Jan-03197.96759.473-680.169-263.297-86.94787.630
Feb-03190.48049.890-696.160-273.078-102.29773.185
Mar-03176.69141.784-709.098-281.395-115.16356.747
Apr-03168.77732.022-739.054-303.608-132.36235.125
May-03164.82120.806-777.522-332.261-149.78512.128
Jun-03156.4448.341-825.476-368.905-175.369-16.206
Jul-03151.6131.637-863.356-396.091-195.228-32.456
Aug-03150.316-1.222-882.774-409.353-202.817-38.196
Sep-03149.016-4.843-900.403-421.448-210.252-43.698
Oct-03147.496-6.111-918.531-431.021-215.041-47.138
Nov-03146.252-8.892-939.810-441.738-220.813-51.026
Dec-03143.305-9.443-962.057-452.065-229.562-56.738

Figure 8a. Trace Cumulative Squared Prediction Errors, 1-Month Forecast Horizon, 1994 - 2003: Yield-Only Models

Data for Figure 8a immediately follows.

Data for Figure 8a

MonthARVARNS2-ARNS2-VARNS1ATSM
Jan-94-0.332-0.471-1.159-0.372-0.496-0.415
Feb-940.5590.6510.8220.5790.4760.400
Mar-941.2741.2492.3311.0600.7430.657
Apr-941.8381.5383.3581.3110.7650.701
May-942.1041.5643.6061.2710.7690.616
Jun-942.1771.2413.4700.8670.0650.143
Jul-942.0531.4823.3531.0500.1670.328
Aug-942.2591.6263.6191.2150.3870.377
Sep-942.6581.6404.0631.1730.1450.260
Oct-942.8461.5174.1100.978-0.1350.059
Nov-943.2471.5724.4271.0470.3570.015
Dec-943.2461.2303.8980.446-0.366-0.429
Jan-953.2252.2344.7111.3550.4630.513
Feb-952.9732.4935.0841.5710.7610.692
Mar-952.9802.5015.1471.6420.8050.662
Apr-952.8372.2955.0221.4890.7930.412
May-952.2671.3634.2210.6420.525-0.543
Jun-952.0960.9243.8780.215-0.064-0.928
Jul-952.2391.1494.0720.4240.006-0.708
Aug-952.0920.7193.7050.077-0.163-1.114
Sep-951.9990.4333.503-0.144-0.301-1.412
Oct-951.7860.0403.194-0.536-0.610-1.821
Nov-951.524-0.5562.774-1.009-0.976-2.456
Dec-951.143-1.3062.181-1.789-1.952-3.109
Jan-961.019-1.4972.065-1.929-2.336-3.274
Feb-961.498-0.3443.195-0.860-1.608-2.113
Mar-961.8250.1513.816-0.314-1.312-1.670
Apr-961.9960.4954.201-0.009-1.192-1.337
May-962.1640.5734.3850.116-1.223-1.316
Jun-962.0120.4714.2780.046-1.135-1.477
Jul-962.1230.5494.3430.118-1.095-1.454
Aug-962.2030.5294.3980.127-1.194-1.512
Sep-961.9670.2954.204-0.034-1.107-1.803
Oct-961.6730.0853.947-0.176-1.012-2.068
Nov-961.437-0.2833.596-0.471-1.228-2.477
Dec-961.7010.0993.935-0.154-1.032-2.108
Jan-971.7220.0843.952-0.145-1.068-2.160
Feb-971.8150.1264.062-0.045-1.028-2.196
Mar-972.1180.2864.2460.117-1.086-2.076
Apr-971.9600.1894.2280.078-0.931-2.242
May-971.8450.0834.152-0.073-1.066-2.359
Jun-971.7480.1084.2650.064-0.956-2.417
Jul-971.423-0.1584.084-0.060-0.802-2.725
Aug-971.6410.0944.2710.148-0.695-2.429
Sep-971.396-0.1784.150-0.075-0.745-2.732
Oct-971.213-0.2544.137-0.076-0.666-2.882
Nov-971.293-0.2274.1730.003-0.605-2.933
Dec-971.172-0.3824.151-0.070-0.621-3.166
Jan-980.853-0.8654.047-0.436-0.928-3.662
Feb-981.011-0.6914.185-0.223-0.776-3.558
Mar-981.015-0.8214.219-0.222-0.791-3.637
Apr-980.926-0.9264.313-0.296-0.712-3.690
May-980.835-1.0364.229-0.458-0.954-3.857
Jun-980.785-0.9844.337-0.313-0.917-3.868
Jul-980.765-1.0264.328-0.385-1.020-3.903
Aug-980.213-1.4244.521-0.634-1.208-4.367
Sep-98-0.588-2.7483.975-1.825-2.563-5.627
Oct-98-0.601-2.7663.887-1.973-3.014-5.609
Nov-98-0.316-2.3844.128-1.619-2.558-5.368
Dec-98-0.375-2.5604.095-1.714-2.736-5.559
Jan-99-0.459-2.7564.070-1.794-2.855-5.738
Feb-990.202-1.7824.544-1.026-2.393-4.815
Mar-990.049-2.0874.495-1.176-2.453-5.073
Apr-990.079-2.0944.565-1.112-2.438-5.153
May-990.376-1.8704.776-0.912-2.408-5.046
Jun-990.483-1.8074.756-0.896-2.403-5.045
Jul-990.550-1.9174.726-0.972-2.532-5.196
Aug-990.665-1.8914.609-1.042-2.699-5.246
Sep-990.538-2.0044.601-1.103-2.876-5.395
Oct-990.653-1.9894.483-1.196-2.994-5.450
Nov-990.853-1.8664.299-1.192-2.805-5.376
Dec-991.036-1.8354.141-1.223-2.810-5.354
Jan-001.236-1.7904.072-1.116-2.694-5.374
Feb-001.198-1.8234.135-1.032-2.606-5.475
Mar-001.101-1.7364.357-0.782-2.427-5.552
Apr-001.167-1.8644.131-0.920-2.564-5.578
May-001.095-2.1713.861-1.452-3.106-5.818
Jun-001.100-0.9964.472-0.360-1.760-4.768
Jul-001.123-0.8574.313-0.187-1.460-4.760
Aug-000.990-1.1774.372-0.334-1.537-5.117
Sep-000.931-1.2064.467-0.416-1.663-5.153
Oct-000.898-1.3594.335-0.561-1.731-5.484
Nov-000.656-2.1084.168-1.219-2.487-6.340
Dec-000.299-3.2013.800-2.258-3.788-7.419
Jan-01-0.101-3.9133.596-2.889-4.961-7.719
Feb-01-0.297-4.6253.010-3.455-5.384-8.412
Mar-01-0.610-5.1492.454-3.859-4.976-8.677
Apr-01-0.590-4.4962.995-3.247-4.356-8.007
May-01-0.797-4.6972.639-3.378-4.661-8.306
Jun-01-0.790-4.7072.570-3.374-4.655-8.470
Jul-01-1.199-5.3761.405-3.912-5.131-9.170
Aug-01-1.508-6.0600.248-4.488-5.604-9.884
Sep-01-2.573-7.562-2.244-5.583-7.050-11.243
Oct-01-3.291-8.949-5.042-6.722-8.484-12.523
Nov-01-3.057-7.738-3.718-5.676-7.351-11.947
Dec-01-2.920-7.502-3.397-5.524-7.115-12.388
Jan-02-2.885-7.482-3.664-5.557-7.148-12.821
Feb-02-3.080-7.742-4.560-5.747-7.371-13.412
Mar-02-2.517-7.026-2.911-5.300-6.638-13.590
Apr-02-2.978-7.263-4.064-5.373-6.731-14.236
May-02-3.132-7.435-4.711-5.464-6.842-14.703
Jun-02-3.486-7.917-6.121-5.845-7.177-15.372
Jul-02-3.985-8.853-8.445-6.541-7.938-15.976
Aug-02-4.310-10.015-10.835-7.503-8.981-16.767
Sep-02-4.938-11.911-14.312-8.992-11.155-17.999
Oct-02-4.946-11.830-14.618-8.844-11.426-17.803
Nov-02-4.757-10.750-13.665-7.837-10.936-17.024
Dec-02-5.307-12.114-16.662-8.889-12.286-17.776
Jan-03-5.216-11.920-16.702-8.634-12.239-17.603
Feb-03-5.484-12.996-18.824-9.429-13.177-18.207
Mar-03-5.540-13.149-19.458-9.457-13.521-18.242
Apr-03-5.582-13.436-20.236-9.587-13.840-18.379
May-03-5.956-15.025-23.080-10.770-15.308-19.255
Jun-03-6.088-15.138-23.793-10.818-16.031-19.221
Jul-03-5.492-13.457-21.092-9.434-14.980-18.092
Aug-03-5.401-13.300-21.241-9.259-14.878-18.060
Sep-03-5.956-14.584-24.442-10.202-16.193-18.716
Oct-03-5.665-13.827-23.377-9.518-15.543-18.252
Nov-03-5.610-13.735-23.549-9.394-15.496-18.253
Dec-03-5.808-14.085-24.683-9.637-15.854-18.512

Figure 8b. Trace Cumulative Squared Prediction Errors, 1-Month Forecast Horizon, 1994 - 2003: Macro Models

Data for Figure 8b immediately follows.

Data for Figure 8b

MonthAR-XVAR-XNS2-AR-XNS2-VAR-XNS1-XATSM-X
Jan-940.056-0.058-0.1820.037-0.064-0.022
Feb-940.2590.3940.320-0.217-0.039-0.636
Mar-94-0.093-0.1370.232-0.933-0.637-2.371
Apr-940.2550.0600.286-1.341-1.081-3.564
May-940.6730.202-0.071-1.886-1.429-5.330
Jun-940.540-0.590-0.722-2.684-2.326-7.314
Jul-940.621-0.195-0.429-2.341-1.987-7.334
Aug-940.651-0.386-0.582-2.587-2.126-8.620
Sep-940.523-1.153-1.259-3.482-3.305-11.265
Oct-940.673-1.427-1.769-4.107-3.965-12.075
Nov-941.009-1.642-2.283-4.753-4.185-13.579
Dec-940.992-2.422-3.357-5.812-5.162-15.857
Jan-951.125-1.403-2.603-4.863-3.922-16.370
Feb-951.571-0.144-1.363-3.697-2.708-14.875
Mar-951.563-0.261-1.549-3.817-2.792-15.535
Apr-951.646-0.116-1.339-3.599-2.539-15.405
May-952.5611.027-0.176-2.529-1.245-14.522
Jun-952.5751.1080.002-2.363-1.262-14.393
Jul-952.5011.034-0.375-2.702-1.519-14.962
Aug-952.5210.968-0.328-2.661-1.398-15.100
Sep-952.5100.906-0.403-2.724-1.400-15.644
Oct-952.4510.990-0.254-2.554-1.224-15.538
Nov-952.5321.110-0.110-2.342-0.888-15.350
Dec-952.9041.7430.579-1.716-0.511-14.724
Jan-962.9421.8480.549-1.648-0.320-14.698
Feb-963.0272.3000.264-2.075-0.596-14.252
Mar-962.9372.111-0.025-2.497-1.187-14.576
Apr-962.9432.146-0.394-2.895-1.648-14.990
May-962.8531.710-1.023-3.532-2.408-16.015
Jun-962.6851.750-0.843-3.345-2.211-16.073
Jul-962.8001.697-1.328-3.801-2.609-17.202
Aug-962.7661.387-1.783-4.225-3.127-18.019
Sep-962.8651.673-1.363-3.818-2.649-17.695
Oct-963.1152.203-0.838-3.258-2.061-17.155
Nov-963.2232.367-0.650-3.051-1.853-17.450
Dec-963.1832.093-1.301-3.673-2.193-17.718
Jan-973.1892.070-1.503-3.859-2.352-18.057
Feb-973.1841.887-1.750-4.111-2.700-18.572
Mar-973.2381.446-2.592-4.937-3.613-19.971
Apr-973.2601.633-2.320-4.674-3.314-19.943
May-973.2941.685-2.301-4.665-3.299-20.248
Jun-973.3991.817-2.155-4.457-3.023-20.354
Jul-973.6332.361-1.434-3.746-2.397-19.171
Aug-973.4531.885-2.374-4.520-2.951-19.832
Sep-973.4072.082-1.975-4.169-2.588-19.556
Oct-973.3232.303-1.771-3.886-2.246-19.288
Nov-973.3092.009-2.346-4.311-2.499-19.877
Dec-973.2882.074-2.390-4.247-2.382-20.065
Jan-983.1942.333-1.839-3.744-1.971-19.449
Feb-983.0421.920-2.488-4.194-2.178-19.831
Mar-983.0101.812-2.891-4.423-2.269-20.149
Apr-983.0281.897-2.865-4.355-2.130-20.145
May-983.0551.808-3.164-4.534-2.219-20.373
Jun-983.0791.901-3.431-4.576-2.015-20.342
Jul-983.0581.720-3.874-4.865-2.182-20.868
Aug-983.9353.341-2.378-3.538-1.137-18.916
Sep-984.5484.476-0.958-2.408-0.682-17.489
Oct-984.5064.327-1.422-2.788-0.915-17.863
Nov-984.2633.758-2.142-3.396-0.975-18.583
Dec-984.2553.727-2.354-3.537-1.025-18.793
Jan-994.2513.710-2.594-3.659-1.014-19.018
Feb-994.1303.071-4.476-5.088-1.803-20.184
Mar-994.0463.082-4.436-5.003-1.758-20.171
Apr-993.9662.903-4.688-5.166-2.093-20.470
May-993.9322.549-5.578-5.878-2.664-21.612
Jun-993.8612.190-6.180-6.359-2.999-22.294
Jul-993.8291.854-6.679-6.770-3.253-22.849
Aug-993.9921.822-7.326-7.273-3.646-23.222
Sep-993.8931.866-7.266-7.204-3.667-23.186
Oct-993.7021.256-7.885-7.702-4.060-24.038
Nov-993.7600.873-8.671-8.291-4.124-24.445
Dec-993.6710.299-9.419-8.850-4.435-24.943
Jan-003.7890.017-10.041-9.271-4.661-25.498
Feb-003.7520.018-10.019-9.186-4.601-25.531
Mar-003.7500.226-9.735-8.849-4.407-25.305
Apr-003.751-0.117-10.245-9.235-4.601-25.508
May-003.724-0.322-10.585-9.676-4.955-25.671
Jun-003.8650.645-10.087-8.800-3.519-24.845
Jul-003.8190.435-10.551-8.972-3.356-25.105
Aug-003.7840.394-10.414-8.857-3.266-25.127
Sep-003.8740.602-10.294-8.729-3.159-24.969
Oct-003.8650.455-10.582-8.935-3.159-25.234
Nov-003.6730.161-10.356-8.897-3.363-25.383
Dec-003.661-0.016-10.028-8.781-3.685-25.311
Jan-014.4491.096-9.317-8.079-3.481-24.623
Feb-014.5700.850-9.656-8.300-3.588-24.779
Mar-014.7400.957-9.731-8.103-3.407-24.332
Apr-014.7761.619-9.075-7.471-2.826-23.682
May-014.8241.694-9.118-7.360-2.961-23.532
Jun-014.8221.704-9.119-7.400-2.975-23.661
Jul-014.8681.478-9.578-7.394-3.022-23.132
Aug-015.0011.295-10.059-7.569-3.191-23.301
Sep-014.3820.300-10.421-7.136-3.895-22.558
Oct-013.828-1.194-12.018-7.723-4.681-22.990
Nov-013.9630.010-10.657-6.726-3.540-22.288
Dec-013.7220.028-10.369-6.703-3.307-22.107
Jan-023.548-0.077-10.465-6.855-3.466-22.285
Feb-023.614-0.026-10.658-6.920-3.632-22.462
Mar-023.422-0.049-10.443-7.182-3.292-22.885
Apr-023.1180.050-10.220-6.766-3.238-23.171
May-023.088-0.005-10.330-6.800-3.387-23.413
Jun-023.1940.022-10.756-6.988-3.659-23.885
Jul-023.432-0.206-11.780-7.586-4.429-25.021
Aug-023.434-1.256-13.211-8.661-5.340-26.515
Sep-023.764-2.287-15.320-10.142-7.053-29.224
Oct-023.605-2.183-15.221-9.935-7.063-29.340
Nov-023.451-1.212-14.141-8.876-6.502-28.315
Dec-023.510-2.185-16.391-10.160-7.529-29.741
Jan-033.521-1.959-16.305-9.910-7.434-29.676
Feb-033.174-3.443-18.283-11.106-8.476-31.190
Mar-033.099-3.742-18.864-11.278-8.886-31.906
Apr-033.094-3.944-19.752-11.615-9.207-32.625
May-033.199-5.238-22.890-13.456-10.808-34.118
Jun-033.190-5.150-23.318-13.563-11.477-34.289
Jul-033.957-2.902-20.795-11.806-10.197-32.382
Aug-034.062-2.857-20.876-11.657-10.167-32.255
Sep-033.416-4.949-23.831-13.357-11.774-33.630
Oct-033.737-3.988-22.742-12.416-11.070-32.494
Nov-033.784-4.037-22.862-12.339-11.129-32.478
Dec-033.553-4.594-23.819-12.840-11.658-33.226

Figure 8c. Trace Cumulative Squared Prediction Errors, 1-Month Forecast Horizon, 1994 - 2003: Forecast Combinations

Data for Figure 8c immediately follows.

Data for Figure 8c

MonthFC-MSPEFC-MSPE-XFC-MSPE-ALLFC-MCS-EW
Jan-94-0.3100.015-0.1380.019
Feb-940.5800.0750.375-0.028
Mar-941.078-0.4530.371-0.320
Apr-941.383-0.5780.466-0.283
May-941.496-0.7100.452-0.156
Jun-941.304-1.2670.071-0.410
Jul-941.479-0.8930.383-0.205
Aug-941.686-1.0300.428-0.100
Sep-941.766-1.7610.084-0.222
Oct-941.754-2.028-0.069-0.213
Nov-942.001-2.236-0.0620.132
Dec-941.738-2.822-0.508-0.006
Jan-952.560-1.8010.5220.563
Feb-952.757-0.7981.2220.855
Mar-952.811-0.8641.2470.885
Apr-952.723-0.6591.3480.876
May-952.1820.2631.6030.996
Jun-951.9270.3971.5851.021
Jul-952.1130.2251.6331.046
Aug-951.9110.2901.5941.024
Sep-951.7820.2701.5430.987
Oct-951.5580.4351.5570.992
Nov-951.2400.6551.5610.949
Dec-950.7681.1901.6871.279
Jan-960.7071.3411.8011.364
Feb-961.5161.3922.2921.449
Mar-961.9101.1732.4111.398
Apr-962.1731.0432.5111.524
May-962.2700.6392.3771.411
Jun-962.2440.7902.4651.435
Jul-962.3250.5972.4221.457
Aug-962.3470.3312.3191.403
Sep-962.2480.6642.4811.500
Oct-962.1431.1202.7101.645
Nov-961.9221.2522.6951.653
Dec-962.2011.0032.7391.683
Jan-972.2200.9502.7371.676
Feb-972.2910.7922.7111.661
Mar-972.4280.2942.5311.601
Apr-972.4280.5152.6701.687
May-972.3620.5742.7001.715
Jun-972.4340.7792.8991.865
Jul-972.3351.3723.2052.021
Aug-972.5300.9573.1251.936
Sep-972.4001.2213.2271.995
Oct-972.3901.4793.3892.063
Nov-972.4571.2653.3432.041
Dec-972.4101.3463.3912.064
Jan-982.1621.6983.4902.080
Feb-982.3231.4433.4752.015
Mar-982.3281.3393.4641.990
Apr-982.3541.4553.5872.143
May-982.2831.4343.5712.162
Jun-982.3921.5623.7252.296
Jul-982.3941.4353.7082.289
Aug-982.2122.6464.3522.986
Sep-981.3903.5334.4613.304
Oct-981.3753.4094.4343.268
Nov-981.7053.0934.4723.175
Dec-981.6493.0734.4653.180
Jan-991.5933.0664.4773.180
Feb-992.1932.3334.4322.979
Mar-992.1002.4114.4532.946
Apr-992.1642.2874.4542.885
May-992.3301.8494.3272.790
Jun-992.3981.5844.2412.690
Jul-992.3701.3674.1292.587
Aug-992.3761.2364.0622.608
Sep-992.3401.3324.1042.576
Oct-992.3430.9793.9332.351
Nov-992.4720.8023.9032.409
Dec-992.5180.4893.7652.319
Jan-002.6010.2813.7002.346
Feb-002.6440.3453.7592.366
Mar-002.7630.5603.9422.388
Apr-002.7330.4053.8472.411
May-002.5350.2783.6772.269
Jun-003.5141.2494.7073.151
Jul-003.6341.1994.7533.194
Aug-003.5291.2614.7383.143
Sep-003.5491.4224.8603.265
Oct-003.4861.3684.8053.242
Nov-003.0701.3154.5573.038
Dec-002.4231.3374.2312.891
Jan-012.0521.9804.4093.482
Feb-011.6711.8924.1693.491
Mar-011.5492.1074.2203.828
Apr-012.0452.6204.7664.206
May-011.8862.6764.7254.273
Jun-011.8972.6784.7384.274
Jul-011.4202.6764.4934.224
Aug-010.9792.5944.2214.285
Sep-01-0.1082.4343.5534.219
Oct-01-1.1661.7552.6073.855
Nov-01-0.3152.5923.5204.160
Dec-01-0.1332.7013.6914.117
Jan-02-0.1092.6363.6903.994
Feb-02-0.3222.6083.5833.999
Mar-020.2682.6123.9243.901
Apr-020.0392.6943.8533.740
May-02-0.0602.6753.8003.731
Jun-02-0.4412.5583.5453.715
Jul-02-1.0932.1672.9893.624
Aug-02-1.8611.4502.1763.487
Sep-02-3.1960.4460.9083.577
Oct-02-3.0730.6201.0763.531
Nov-02-2.3171.4031.9043.449
Dec-02-3.2720.5890.9393.463
Jan-03-3.0440.8231.1763.475
Feb-03-3.697-0.0880.3093.280
Mar-03-3.737-0.2330.1903.248
Apr-03-3.837-0.3830.0383.244
May-03-4.814-1.473-1.1023.259
Jun-03-4.897-1.459-1.1453.208
Jul-03-3.6570.0920.3613.563
Aug-03-3.4860.2590.5353.630
Sep-03-4.424-1.082-0.7183.302
Oct-03-3.797-0.2580.0613.464
Nov-03-3.694-0.1870.1523.489
Dec-03-3.947-0.600-0.2183.385

Figure 9a. Trace Cumulative Squared Prediction Errors, 3-Month Forecast Horizon, 1994 - 2003: Yield-Only Models

Data for Figure 9a immediately follows.

Data for Figure 9a

MonthARVARNS2-ARNS2-VARNS1ATSM
Jan-94#N/A#N/A#N/A#N/A#N/A#N/A
Feb-94#N/A#N/A#N/A#N/A#N/A#N/A
Mar-943.9025.6107.8873.9273.7173.663
Apr-9410.77515.75621.69810.49210.92510.053
May-9415.61921.33430.20413.96214.71413.476
Jun-9418.37323.42034.62715.00915.21614.441
Jul-9418.93423.76535.14115.14915.37014.524
Aug-9419.36724.22635.65815.49415.75314.777
Sep-9420.76824.56736.93215.40215.94114.629
Oct-9423.26425.64339.52415.65916.38114.904
Nov-9426.52527.93943.32316.96617.88616.265
Dec-9428.38928.40944.69416.79818.08516.243
Jan-9529.37329.65145.81417.80019.70117.229
Feb-9528.57831.51747.90019.92821.89719.139
Mar-9527.97335.36052.46424.04625.38223.019
Apr-9526.94135.69753.87824.79226.38623.458
May-9524.98133.84753.36723.71525.73921.947
Jun-9522.64230.70051.91521.50525.00919.235
Jul-9520.90327.62950.05619.15123.49816.604
Aug-9520.38725.92249.25617.88521.88815.312
Sep-9520.07524.69448.76217.09021.12614.397
Oct-9518.78721.30046.10714.42919.29811.503
Nov-9517.16617.35243.61111.54417.2898.200
Dec-9514.74112.43241.1907.80714.0364.222
Jan-9612.5297.65238.7724.22610.1560.391
Feb-9612.4107.20439.0274.0489.4030.414
Mar-9614.48810.90541.4417.04312.3263.595
Apr-9617.55718.21247.69813.13617.4169.975
May-9619.63022.17851.40116.46319.67913.387
Jun-9620.14623.05052.30217.20420.02214.208
Jul-9620.48823.35852.60317.48020.13814.461
Aug-9620.58923.35152.70917.52520.02914.412
Sep-9620.38223.04052.64217.38419.82514.186
Oct-9619.05921.65751.93016.60619.62613.136
Nov-9617.03519.79550.68215.71620.19211.738
Dec-9616.21118.85950.11115.21920.08010.995
Jan-9716.31418.84450.28015.31520.05111.034
Feb-9717.45520.55851.55216.68521.10512.509
Mar-9718.74422.05952.63817.77621.75213.694
Apr-9719.38022.79453.29118.34221.96914.291
May-9719.37422.67653.38118.22621.74214.197
Jun-9718.33621.67653.15317.81222.06413.389
Jul-9716.83620.55052.99717.48022.32012.676
Aug-9716.16720.21953.08917.51222.30112.498
Sep-9715.07718.85252.62816.75122.28811.489
Oct-9714.37917.46452.27015.92521.76310.435
Nov-9713.37816.11651.89515.26821.7019.355
Dec-9712.73015.47551.81115.19321.9108.925
Jan-9811.64413.47951.34114.09821.1327.396
Feb-9810.80712.10651.32413.46220.7646.383
Mar-9810.32810.94151.29012.89720.2315.576
Apr-9810.51811.03951.73513.06520.0785.872
May-9810.0099.88651.75812.27919.3125.076
Jun-989.3148.23251.56711.39118.9943.849
Jul-988.8247.45551.50911.03018.5833.318
Aug-986.9695.48952.21710.21117.0532.095
Sep-983.149-0.35952.9626.78414.508-2.207
Oct-98-0.567-5.17354.1214.07112.073-5.586
Nov-98-2.169-8.64253.4241.8779.744-8.008
Dec-98-1.556-7.92753.5972.57710.221-7.294
Jan-99-1.176-7.92053.9263.00910.557-7.017
Feb-990.382-5.10155.3155.06912.297-4.731
Mar-991.584-3.07056.0676.43013.390-3.078
Apr-993.111-0.26557.0968.20914.467-0.860
May-993.6340.19457.2518.41014.133-0.584
Jun-994.9632.25558.4599.78814.5481.044
Jul-996.3904.20059.48210.95614.9922.428
Aug-997.2654.92559.38811.13514.9082.846
Sep-997.3934.87159.33611.04914.7132.761
Oct-997.6775.07259.24011.04114.5192.821
Nov-998.2215.53958.97411.18514.7303.100
Dec-999.7736.89458.78411.75414.8953.965
Jan-0011.6538.09857.75512.12515.8574.586
Feb-0012.6938.93357.18212.64216.5635.125
Mar-0012.8729.36057.17813.30117.4685.429
Apr-0012.6249.23157.18713.42317.7295.298
May-0012.2808.67757.08612.83517.1564.791
Jun-0012.0678.36656.81512.64217.0364.589
Jul-0011.8099.21556.70613.68018.1405.380
Aug-0011.65612.84458.32017.56822.2208.896
Sep-0011.14112.75858.52417.73022.5908.846
Oct-0010.49011.41658.62116.83722.1317.669
Nov-009.5198.93558.90115.13520.6165.430
Dec-007.7614.72258.81511.78316.8241.708
Jan-015.345-1.48459.0816.52410.287-3.415
Feb-012.932-8.09558.4721.0463.532-8.695
Mar-010.648-13.41057.212-3.133-2.045-12.454
Apr-01-0.649-14.85756.156-4.066-3.931-13.122
May-01-1.802-14.95855.860-3.869-0.127-12.453
Jun-01-2.224-14.22056.262-2.9770.566-11.465
Jul-01-4.012-17.44252.098-5.182-1.885-13.860
Aug-01-6.098-21.07946.910-7.496-3.844-16.471
Sep-01-11.079-28.24337.045-12.437-8.956-21.610
Oct-01-16.828-38.99421.541-20.366-16.983-29.585
Nov-01-21.058-45.02712.778-24.214-22.124-33.793
Dec-01-22.007-45.40310.341-23.809-22.448-34.013
Jan-02-20.751-41.07414.419-19.996-18.478-30.896
Feb-02-20.842-41.59012.156-19.970-18.437-31.337
Mar-02-19.651-40.03714.034-18.803-17.148-30.882
Apr-02-20.050-41.05011.416-19.115-17.420-31.878
May-02-20.336-41.8109.239-19.233-17.508-32.500
Jun-02-23.102-44.2793.066-19.613-17.773-33.510
Jul-02-26.020-48.607-6.832-21.490-19.437-35.485
Aug-02-29.405-53.761-18.439-23.930-21.645-37.711
Sep-02-33.611-62.174-35.689-28.782-26.392-41.967
Oct-02-36.438-70.592-52.353-34.576-33.659-46.898
Nov-02-37.708-73.311-58.920-35.705-36.174-48.013
Dec-02-38.793-76.262-65.112-36.846-38.665-48.854
Jan-03-39.583-78.794-71.876-37.838-40.715-49.635
Feb-03-41.737-84.837-83.725-41.189-45.163-52.464
Mar-03-42.433-87.955-90.631-42.619-47.441-53.610
Apr-03-43.514-91.928-99.052-44.663-50.350-55.341
May-03-44.926-97.682-109.115-47.763-54.774-57.926
Jun-03-46.556-103.177-119.898-50.641-58.934-60.359
Jul-03-46.212-101.998-120.769-49.108-57.828-58.976
Aug-03-44.553-95.365-114.355-44.364-52.777-54.504
Sep-03-44.172-94.988-115.547-43.607-52.383-53.706
Oct-03-44.700-96.995-122.386-44.541-53.807-54.460
Nov-03-45.317-98.730-128.351-45.223-55.062-55.097
Dec-03-44.888-97.965-129.649-44.194-54.274-54.206

Figure 9b. Trace Cumulative Squared Prediction Errors, 3-Month Forecast Horizon, 1994 - 2003: Macro Models

Data for Figure 9b immediately follows.

Data for Figure 9b

MonthAR-XVAR-XNS2-AR-XNS2-VAR-XNS1-XATSM-X
Jan-94#N/A#N/A#N/A#N/A#N/A#N/A
Feb-94#N/A#N/A#N/A#N/A#N/A#N/A
Mar-94-1.8180.8941.560-1.685-0.682-0.793
Apr-94-2.0502.6453.659-4.990-0.750-2.613
May-94-3.9862.6452.602-9.591-2.547-7.704
Jun-94-2.0853.3742.439-12.107-4.242-9.897
Jul-94-1.4773.4291.609-13.607-5.150-11.467
Aug-94-1.8353.1880.363-15.240-6.004-13.804
Sep-94-1.9422.429-2.091-18.559-8.464-19.121
Oct-94-3.1780.899-5.849-23.602-13.006-25.371
Nov-94-4.143-0.413-9.730-28.761-18.458-32.622
Dec-94-3.199-1.246-12.854-32.767-21.643-36.567
Jan-95-2.773-1.250-13.452-33.727-21.744-38.011
Feb-95-1.8580.908-9.956-30.033-17.951-34.268
Mar-95-0.7774.607-5.420-24.768-12.250-29.408
Apr-950.8706.445-2.312-21.487-8.811-26.084
May-952.0848.0542.132-17.253-4.244-21.514
Jun-954.3609.6897.363-12.4251.407-15.975
Jul-956.15110.39610.202-9.7464.139-13.698
Aug-956.11910.51210.119-9.7374.298-13.813
Sep-956.11010.4938.919-10.7514.095-14.731
Oct-956.50210.3719.315-10.3874.917-14.661
Nov-956.30610.2549.959-9.6506.085-15.132
Dec-956.27910.72313.144-6.6778.457-12.379
Jan-966.93711.32815.555-4.24910.357-10.006
Feb-966.43111.76814.905-4.60510.346-10.070
Mar-965.86011.4467.760-11.1199.072-13.184
Apr-965.14612.4424.485-14.8137.514-13.512
May-964.94812.6492.196-17.7055.170-14.605
Jun-964.71612.647-0.286-20.0243.084-16.040
Jul-964.32312.200-3.117-22.6970.586-18.167
Aug-964.41412.025-5.205-24.534-1.310-19.566
Sep-964.41911.952-6.409-25.594-2.164-20.653
Oct-964.98212.705-4.795-23.941-0.398-19.197
Nov-966.49813.994-1.017-20.2583.730-16.077
Dec-966.94814.335-0.703-19.8494.222-15.825
Jan-976.70514.186-2.109-21.1113.418-16.682
Feb-976.61413.927-5.834-24.2841.940-17.949
Mar-976.84813.375-9.472-27.710-0.868-20.075
Apr-976.47912.977-11.457-29.655-2.949-21.653
May-976.38512.838-12.797-30.918-4.208-22.807
Jun-976.60913.283-11.506-29.618-2.813-21.875
Jul-977.96414.404-8.857-26.911-0.112-19.614
Aug-978.43214.875-9.138-26.8220.447-19.673
Sep-978.85315.257-8.356-25.9161.501-18.633
Oct-979.05315.381-9.339-26.4031.429-18.951
Nov-978.92615.626-9.174-25.9022.318-18.278
Dec-979.13215.875-10.367-26.3532.626-18.390
Jan-989.52916.159-10.447-25.9733.283-18.267
Feb-989.52016.382-11.173-25.9953.645-18.295
Mar-989.51516.405-12.694-26.7023.425-18.784
Apr-989.24116.397-15.163-28.2022.800-19.476
May-989.20516.462-16.808-28.9632.576-19.841
Jun-989.41716.513-18.088-29.4432.436-20.080
Jul-989.50116.529-20.580-30.7072.270-20.697
Aug-989.59117.550-18.319-28.1344.164-18.367
Sep-9813.16920.096-9.578-20.99310.235-11.834
Oct-9817.75123.170-0.830-13.59516.147-4.377
Nov-9818.52823.5420.126-12.53017.006-3.334
Dec-9818.17323.240-4.569-16.08815.968-5.824
Jan-9917.83923.180-7.257-18.16715.604-7.319
Feb-9918.10323.501-12.887-22.13914.694-9.294
Mar-9917.65623.470-19.085-26.41313.366-12.215
Apr-9917.52523.575-25.521-30.72811.063-14.065
May-9917.23323.115-29.724-33.6718.218-16.313
Jun-9916.03622.790-34.008-36.7394.885-18.549
Jul-9915.62922.473-38.665-40.1692.280-21.243
Aug-9914.55121.648-43.096-43.684-0.316-24.044
Sep-9914.55621.416-45.341-45.280-1.129-25.085
Oct-9914.87221.349-47.659-46.928-2.079-25.761
Nov-9914.84720.944-50.810-49.121-3.163-27.561
Dec-9913.47119.828-55.762-52.744-5.755-30.655
Jan-0012.98218.483-61.788-57.333-7.573-33.634
Feb-0012.31917.545-65.782-60.055-9.078-35.510
Mar-0012.53417.458-66.957-60.525-8.943-35.741
Apr-0012.55517.525-67.463-60.608-8.933-35.716
May-0012.53217.601-67.979-60.990-9.196-35.875
Jun-0012.54717.630-69.203-61.510-9.434-36.051
Jul-0012.54918.073-70.037-61.267-8.848-35.297
Aug-0013.26120.118-69.451-58.795-4.740-32.171
Sep-0013.43520.503-69.968-58.543-4.149-31.753
Oct-0013.66920.692-69.858-58.288-3.838-31.631
Nov-0014.24720.961-69.007-57.644-3.680-31.414
Dec-0014.68220.819-66.419-56.029-4.391-30.783
Jan-0112.68720.806-60.660-52.563-4.468-29.613
Feb-0115.01021.537-56.024-49.451-3.894-28.030
Mar-0118.33222.791-52.446-46.289-2.529-25.535
Apr-0119.51423.649-51.137-44.421-1.431-23.431
May-0120.25424.990-48.770-41.3500.706-20.215
Jun-0120.27525.914-47.151-39.5852.048-18.358
Jul-0120.11525.160-48.382-39.4661.298-18.082
Aug-0119.81924.170-49.952-39.2370.927-17.951
Sep-0120.73923.205-51.741-37.2661.222-14.694
Oct-0120.19620.361-56.235-37.323-1.445-15.518
Nov-0117.41418.786-56.101-34.998-2.715-14.027
Dec-0117.26219.420-55.454-33.577-1.832-12.587
Jan-0218.91422.408-50.576-30.0102.371-9.060
Feb-0218.74122.610-50.506-30.0222.572-8.966
Mar-0217.99123.335-49.157-30.1053.047-8.966
Apr-0217.88923.309-49.293-30.3782.945-9.199
May-0217.93123.372-49.232-30.4693.028-9.328
Jun-0216.25823.100-48.055-28.5023.461-9.002
Jul-0216.12022.250-50.119-29.0392.095-9.814
Aug-0217.16321.460-53.628-30.4920.182-12.415
Sep-0217.97218.984-61.384-35.331-4.520-18.330
Oct-0218.24016.037-70.688-41.900-10.569-24.392
Nov-0218.51515.970-72.895-42.804-11.520-25.470
Dec-0218.56115.873-74.966-43.620-12.331-26.110
Jan-0318.54915.653-78.165-44.940-13.200-27.467
Feb-0319.18213.876-86.200-49.154-16.604-30.736
Mar-0319.03513.062-91.346-51.532-18.691-32.655
Apr-0317.62211.344-98.653-55.291-22.473-36.390
May-0316.5128.946-108.041-60.419-27.548-41.230
Jun-0316.5097.020-119.298-66.062-32.150-45.568
Jul-0316.5578.221-120.227-64.956-31.162-44.072
Aug-0316.69112.222-113.505-59.611-25.711-39.184
Sep-0316.93312.959-113.582-58.866-25.679-38.506
Oct-0316.05611.959-119.239-61.262-27.985-40.334
Nov-0315.32311.148-124.284-63.321-29.983-41.715
Dec-0315.76112.062-124.962-62.611-29.757-40.883

Figure 9c. Trace Cumulative Squared Prediction Errors, 3-Month Forecast Horizon, 1994 - 2003: Forecast Combinations

Data for Figure 9c immediately follows.

Notes: Figures 8 and 9 show the Trace Cumulative Squared Prediction Error [TCSPE], relative to the random walk, of individual yield-only models in Panel (a), individual models with macro factors in Panel (b) and of forecast combinations schemes in Panel (c). Figure 8 shows TCSPEs for a 1-month forecast horizon whereas Figure 9 does so for a 3-month horizon. The forecast sample is 1994:1 - 2003:12.

Data for Figure 9c

MonthFC-MSPEFC-MSPE-XFC-MSPE-ALLFC-MCS-EW
Jan-94#N/A#N/A#N/A#N/A
Feb-94#N/A#N/A#N/A#N/A
Mar-943.847-0.4001.821-0.657
Apr-9410.407-0.6465.023-1.079
May-9414.229-2.6105.863-2.626
Jun-9415.814-2.9166.494-2.487
Jul-9416.230-3.1246.617-2.308
Aug-9416.735-3.7516.637-2.431
Sep-9417.325-5.3166.087-2.826
Oct-9418.367-8.1265.085-3.938
Nov-9420.206-11.1564.337-4.947
Dec-9420.833-12.7033.769-4.794
Jan-9521.934-12.7624.295-4.278
Feb-9523.361-9.8396.805-3.079
Mar-9526.410-5.21211.171-0.895
Apr-9526.868-2.52213.1900.233
May-9525.8730.47814.5830.796
Jun-9524.1994.09416.0251.809
Jul-9522.4916.06116.5442.161
Aug-9521.7366.29816.6152.219
Sep-9521.2916.13616.6002.221
Oct-9519.4796.62416.2351.993
Nov-9517.4067.13315.7031.521
Dec-9514.7259.04315.7871.578
Jan-9612.08210.74215.8401.750
Feb-9612.19610.85516.5362.414
Mar-9614.7708.80817.0562.472
Apr-9619.6227.95419.3603.767
May-9622.2866.98920.3864.093
Jun-9622.9706.14420.5244.055
Jul-9623.2594.95020.2383.672
Aug-9623.3464.35420.0943.577
Sep-9623.2604.06120.0823.570
Oct-9622.5805.33820.6764.142
Nov-9621.7197.92921.9065.397
Dec-9621.2888.43222.2045.693
Jan-9721.4227.96422.2305.718
Feb-9722.6236.89622.4605.983
Mar-9723.6245.49222.3285.922
Apr-9724.1564.51322.2205.748
May-9724.1564.02022.1115.672
Jun-9723.7935.00222.6206.121
Jul-9723.3607.00023.7377.182
Aug-9723.2947.52724.2507.670
Sep-9722.7158.46924.7178.172
Oct-9722.1328.59924.7988.268
Nov-9721.5789.30825.0978.494
Dec-9721.4349.64525.4228.828
Jan-9820.57510.19725.5698.973
Feb-9820.08910.57625.7619.093
Mar-9819.70310.52425.8149.080
Apr-9819.99210.06925.9769.244
May-9819.55810.06026.0589.358
Jun-9818.99010.18026.1299.453
Jul-9818.74010.09226.1729.542
Aug-9817.93711.94827.05410.110
Sep-9815.33916.96329.00112.294
Oct-9813.17522.34431.41614.964
Nov-9811.57523.27031.47715.081
Dec-9812.26622.03831.46515.037
Jan-9912.70221.39031.60415.039
Feb-9914.49620.26132.10015.428
Mar-9915.76518.66132.12515.311
Apr-9917.35317.11632.30815.398
May-9917.63615.70031.88014.857
Jun-9918.84313.97131.73114.253
Jul-9919.94012.32431.53713.968
Aug-9920.31810.51130.86712.946
Sep-9920.3509.97230.69012.813
Oct-9920.4769.63030.60113.004
Nov-9920.7758.76430.34112.969
Dec-9921.4766.72229.63012.123
Jan-0022.2064.74328.91911.782
Feb-0022.7393.38228.48711.360
Mar-0023.1603.36928.72811.741
Apr-0023.2493.53628.89912.039
May-0022.9773.54128.80812.079
Jun-0022.9303.47328.82012.077
Jul-0023.6614.01229.51812.671
Aug-0026.5356.67232.46615.564
Sep-0026.6907.13932.87015.798
Oct-0026.1707.43732.85615.713
Nov-0025.0897.95532.69815.516
Dec-0022.8488.65232.01814.565
Jan-0119.5089.59930.89712.158
Feb-0115.99011.37330.23012.284
Mar-0113.23413.57330.23413.732
Apr-0112.53714.88730.77415.109
May-0113.38316.86132.37817.370
Jun-0114.12518.04233.48618.518
Jul-0112.11617.76032.35718.001
Aug-019.90417.42131.08817.292
Sep-015.09718.03029.10617.199
Oct-01-1.95416.67324.78715.619
Nov-01-5.88516.50122.75314.272
Dec-01-5.91317.37223.27715.209
Jan-02-2.58820.52726.75518.054
Feb-02-2.60820.69526.93018.079
Mar-02-1.24620.99727.92018.019
Apr-02-1.65020.93927.83317.965
May-02-1.84221.02327.90418.080
Jun-02-3.22721.33927.45017.392
Jul-02-5.81020.62825.80116.590
Aug-02-8.99919.51823.60915.915
Sep-02-14.30116.34519.10413.352
Oct-02-19.65312.63114.19610.543
Nov-02-21.04712.46913.42510.778
Dec-02-22.25512.43512.82211.224
Jan-03-23.26212.12712.08011.342
Feb-03-26.7579.8768.98110.578
Mar-03-28.1028.7617.55710.199
Apr-03-30.1046.3395.0268.736
May-03-33.0393.1641.5827.037
Jun-03-35.9140.313-1.6336.050
Jul-03-34.5971.625-0.3017.067
Aug-03-30.1675.6774.2439.271
Sep-03-29.3846.4124.9719.689
Oct-03-30.3465.0463.5978.978
Nov-03-31.2343.8382.3738.352
Dec-03-30.2824.7133.2719.074

Figure 10a. Trace Cumulative Squared Prediction Errors, 6-Month Forecast Horizon, 1994 - 2003: Yield-Only Models

Data for Figure 10a immediately follows.

Data for Figure 10a

MonthARVARNS2-ARNS2-VARNS1ATSM
Jan-94#N/A#N/A#N/A#N/A#N/A#N/A
Feb-94#N/A#N/A#N/A#N/A#N/A#N/A
Mar-94#N/A#N/A#N/A#N/A#N/A#N/A
Apr-94#N/A#N/A#N/A#N/A#N/A#N/A
May-94#N/A#N/A#N/A#N/A#N/A#N/A
Jun-9413.89322.28824.54212.97113.89612.805
Jul-9428.34445.69548.28126.14128.70126.120
Aug-9438.51059.54763.13633.97637.55534.092
Sep-9447.03669.01075.36038.37641.46938.709
Oct-9453.32574.31482.44539.91644.39340.548
Nov-9460.91180.89289.81642.19848.37943.185
Dec-9467.90086.18496.42743.50150.95844.851
Jan-9575.04894.003104.32047.78956.29149.350
Feb-9578.37598.287108.05050.89860.31152.587
Mar-9579.658101.406110.09453.76063.75255.472
Apr-9579.231104.018111.17156.93767.07458.549
May-9575.150107.176118.05462.88473.81063.333
Jun-9570.803113.913134.02272.84281.93371.910
Jul-9566.318111.155137.64572.82182.80770.823
Aug-9561.788104.419136.04568.92579.14066.195
Sep-9556.94596.182133.04363.74675.89560.137
Oct-9551.68385.801128.04356.67270.43852.393
Nov-9547.56572.796121.90847.74661.14442.924
Dec-9542.23458.759115.85938.44952.08433.096
Jan-9635.82642.677105.69427.29842.52821.294
Feb-9632.46933.948102.13521.86737.38015.507
Mar-9631.38730.017101.71019.96035.07613.412
Apr-9632.60631.335103.96621.62235.33115.282
May-9636.69139.867110.82329.02641.21323.144
Jun-9641.83549.077116.16035.86047.53030.444
Jul-9648.53062.518126.87246.85257.65841.690
Aug-9652.72469.583132.98352.70362.37047.680
Sep-9653.27669.500133.83653.30462.62848.231
Oct-9651.14865.709132.06251.65461.53846.143
Nov-9647.21160.115129.33549.28761.14842.924
Dec-9645.21256.831128.19947.87959.96441.141
Jan-9742.89053.085126.97646.06158.64138.899
Feb-9740.75449.866125.71144.64758.06636.961
Mar-9741.53550.331126.45545.26158.30037.505
Apr-9743.05552.000128.21746.89659.49139.188
May-9745.26855.101130.68849.45561.32542.014
Jun-9745.23854.137130.89749.38761.00941.751
Jul-9743.13849.582129.01147.28059.80539.094
Aug-9741.75046.729128.36046.08559.03537.510
Sep-9737.95141.655127.09343.80658.78234.417
Oct-9733.95036.217126.09741.52357.62931.387
Nov-9730.89232.491125.79340.47856.70729.641
Dec-9727.70426.922124.21438.11856.32126.413
Jan-9824.33918.726122.19233.87253.33921.312
Feb-9820.95312.373120.75130.99752.01417.513
Mar-9818.7978.059120.34229.58451.17015.413
Apr-9817.0443.153119.91027.35149.02412.736
May-9814.463-2.877119.80624.39346.4209.226
Jun-9812.215-9.316119.36721.30343.5675.524
Jul-9811.596-13.198119.39419.87742.0363.953
Aug-987.002-24.942117.97313.54836.966-3.342
Sep-98-1.549-44.357115.5862.79430.533-15.986
Oct-98-9.699-59.391116.025-4.43523.756-24.664
Nov-98-16.054-71.066117.479-9.40617.284-30.782
Dec-98-22.324-84.785118.002-16.04911.863-38.799
Jan-99-28.805-97.582119.028-21.9116.622-45.884
Feb-99-28.876-99.814119.979-22.0275.774-46.065
Mar-99-25.190-93.708121.353-17.5699.950-41.250
Apr-99-21.332-87.774125.135-12.53414.622-36.117
May-99-17.136-79.898128.731-6.86319.493-29.997
Jun-99-11.977-70.096131.169-0.86524.695-23.162
Jul-99-5.890-57.703134.5536.43929.869-14.633
Aug-99-3.023-53.624135.3738.77530.530-11.766
Sep-99-0.175-49.518137.75511.73231.981-8.395
Oct-993.216-44.469140.02914.93733.983-4.758
Nov-996.077-40.938140.37216.79635.127-2.370
Dec-999.484-36.738140.88218.91436.9490.278
Jan-0013.918-31.473141.48621.29837.7173.422
Feb-0017.226-27.724141.15023.18939.7525.752
Mar-0020.715-23.466141.30725.98542.0318.800
Apr-0023.672-20.336140.11127.56744.05710.733
May-0024.702-19.801138.95727.52943.90710.934
Jun-0024.545-20.108138.73627.94544.63811.089
Jul-0023.650-20.594139.23928.83746.41011.247
Aug-0022.215-22.309139.76528.98047.39510.519
Sep-0020.814-24.676139.97928.33447.6389.317
Oct-0019.204-24.695141.41930.13050.30810.334
Nov-0017.205-20.541147.37736.72255.85315.884
Dec-0013.087-26.350152.17234.87455.26612.656
Jan-017.540-38.624157.62327.00049.0213.997
Feb-011.699-53.534162.19917.20339.512-6.951
Mar-01-4.915-69.086165.2376.19125.535-18.135
Apr-01-10.291-82.658168.769-4.00911.881-27.849
May-01-15.328-94.713172.292-12.839-1.079-35.694
Jun-01-19.324-102.877174.084-17.827-9.689-39.879
Jul-01-24.823-115.023167.894-24.999-18.684-46.955
Aug-01-30.746-128.928160.120-33.248-16.007-54.912
Sep-01-40.778-149.483145.388-45.122-27.711-66.689
Oct-01-54.623-175.019121.573-59.692-44.752-81.492
Nov-01-66.363-195.372101.672-70.116-55.263-92.908
Dec-01-77.112-213.15884.693-79.602-65.821-103.017
Jan-02-85.515-228.42267.442-87.334-74.935-110.953
Feb-02-93.537-243.51752.415-94.352-84.401-118.333
Mar-02-92.790-241.73053.567-90.559-81.098-115.500
Apr-02-91.067-239.09755.148-85.699-76.293-111.475
May-02-91.776-243.93948.262-85.895-76.636-112.234
Jun-02-95.368-254.03732.985-88.334-79.251-115.300
Jul-02-101.931-268.97711.761-92.630-84.276-119.822
Aug-02-109.236-286.213-11.925-97.806-90.424-125.001
Sep-02-122.072-303.746-37.820-98.959-91.076-126.769
Oct-02-132.973-325.609-69.117-105.447-96.793-133.450
Nov-02-141.996-344.894-94.794-111.647-102.706-140.002
Dec-02-152.271-369.939-129.883-120.896-112.336-148.991
Jan-03-159.265-392.694-164.994-130.666-126.007-157.629
Feb-03-165.980-416.273-194.599-139.678-139.965-165.696
Mar-03-169.399-432.455-211.991-143.546-146.866-168.975
Apr-03-173.044-449.932-235.558-148.797-155.192-173.441
May-03-180.088-474.531-267.660-157.085-166.880-180.721
Jun-03-184.716-495.639-294.004-163.409-176.780-186.154
Jul-03-186.079-504.197-306.590-164.104-178.926-186.750
Aug-03-185.326-505.531-309.772-160.880-176.283-183.787
Sep-03-187.677-518.743-327.913-163.563-181.151-186.030
Oct-03-188.012-524.515-337.668-162.734-181.656-185.222
Nov-03-185.917-520.427-334.120-157.028-175.887-179.705
Dec-03-184.316-520.501-335.030-153.799-172.853-176.657

Figure 10b. Trace Cumulative Squared Prediction Errors, 6-Month Forecast Horizon, 1994 - 2003: Macro Models

Data for Figure 10b immediately follows.

Data for Figure 10b

MonthAR-XVAR-XNS2-AR-XNS2-VAR-XNS1-XATSM-X
Jan-94#N/A#N/A#N/A#N/A#N/A#N/A
Feb-94#N/A#N/A#N/A#N/A#N/A#N/A
Mar-94#N/A#N/A#N/A#N/A#N/A#N/A
Apr-94#N/A#N/A#N/A#N/A#N/A#N/A
May-94#N/A#N/A#N/A#N/A#N/A#N/A
Jun-94-6.7174.2401.677-8.447-1.700-3.371
Jul-94-9.2438.7842.747-17.794-1.589-7.102
Aug-94-12.67510.678-0.800-28.308-4.640-14.732
Sep-94-8.33712.560-1.340-35.245-7.065-17.517
Oct-94-5.32512.443-7.433-45.163-12.752-23.371
Nov-94-10.10211.030-20.032-60.459-23.203-37.642
Dec-94-11.6899.883-29.537-73.443-32.481-52.202
Jan-95-14.6449.518-36.976-83.923-40.116-62.581
Feb-95-15.1499.734-40.298-88.701-43.763-67.197
Mar-95-13.76610.528-40.170-89.326-42.560-67.121
Apr-95-12.35111.936-37.125-86.293-38.378-63.964
May-95-7.96817.274-19.637-69.131-21.223-47.377
Jun-95-2.47526.3115.559-43.9722.203-22.796
Jul-953.96730.06118.920-31.07915.626-9.985
Aug-957.11131.60025.940-24.27022.694-3.269
Sep-9511.49232.87133.564-16.95730.8603.977
Oct-9515.93733.65340.736-10.15937.9329.602
Nov-9517.06433.27641.252-9.51739.22510.208
Dec-9517.94633.11444.354-6.45441.97612.557
Jan-9620.55632.83249.255-1.74246.70516.459
Feb-9620.56632.94349.484-1.05948.13617.224
Mar-9620.29733.09243.872-5.02646.92215.195
Apr-9618.61233.35733.947-12.57843.68310.158
May-9611.94234.33421.073-22.66238.0933.376
Jun-9610.31534.5400.036-40.69533.912-4.351
Jul-967.10236.096-12.786-53.06729.573-9.208
Aug-966.06136.835-20.428-61.18425.239-12.396
Sep-965.12536.780-27.715-67.46220.799-15.588
Oct-965.69837.005-29.705-68.97620.284-16.164
Nov-965.99237.743-26.315-65.43724.507-13.530
Dec-966.46537.996-27.583-66.27724.476-13.851
Jan-977.26338.391-27.886-66.09125.030-13.305
Feb-978.18238.710-28.123-65.93225.467-13.077
Mar-975.90238.227-35.168-72.26219.783-17.854
Apr-974.33538.052-42.068-78.32416.066-21.315
May-973.75538.080-51.474-85.79512.927-23.955
Jun-973.53537.904-55.782-89.53610.616-25.785
Jul-974.12337.906-56.300-89.82211.008-26.006
Aug-974.31937.963-58.078-91.20110.162-26.708
Sep-975.65338.790-53.674-86.90214.810-23.319
Oct-978.73139.966-49.370-82.40419.659-19.466
Nov-9710.96640.977-48.383-80.65022.541-17.544
Dec-9712.58941.427-47.831-79.35324.920-15.438
Jan-9813.97541.650-49.342-79.55925.990-15.245
Feb-9814.51142.038-49.050-78.28228.419-13.385
Mar-9815.14742.327-52.925-80.17528.568-13.770
Apr-9815.29242.356-57.699-82.84827.410-15.073
May-9815.62242.592-60.542-83.79327.593-15.070
Jun-9816.03042.686-64.173-85.29927.464-15.476
Jul-9815.81342.709-70.817-89.06026.250-17.016
Aug-9817.19743.026-69.333-86.50629.152-14.522
Sep-9821.17243.748-56.289-75.93638.940-7.225
Oct-9821.84844.930-44.168-65.27646.244-0.724
Nov-9822.85046.277-37.430-58.28751.2124.871
Dec-9827.50347.497-31.136-51.86757.45810.749
Jan-9932.80449.009-24.011-44.58664.31417.831
Feb-9931.68049.348-31.828-49.27862.71315.406
Mar-9928.79449.886-50.389-63.10157.6666.994
Apr-9926.42950.966-63.467-73.11054.6521.338
May-9926.57752.198-79.815-83.85552.361-2.315
Jun-9925.10452.966-102.400-98.98246.876-10.179
Jul-9924.02754.213-124.809-113.37739.304-14.935
Aug-9921.54453.791-140.209-123.84629.811-21.387
Sep-9918.70754.038-151.160-131.32922.435-25.814
Oct-9917.23854.152-163.129-139.67216.562-30.762
Nov-9913.92053.561-175.716-149.1949.489-37.115
Dec-9913.78253.059-187.823-157.8384.899-41.504
Jan-0017.14052.831-199.774-166.2680.440-43.724
Feb-0015.83951.916-211.355-174.358-4.116-48.939
Mar-0013.87651.473-221.590-181.289-8.925-54.046
Apr-0012.87450.649-231.778-188.650-12.087-58.170
May-0011.67149.897-238.837-193.581-15.265-61.410
Jun-0011.92249.888-241.413-194.837-15.431-61.859
Jul-0012.42750.349-241.977-194.150-14.191-60.756
Aug-0012.85550.703-241.940-193.150-12.725-59.523
Sep-0013.16751.168-243.717-193.176-12.186-59.081
Oct-0013.32152.445-243.568-191.131-9.475-56.427
Nov-0014.98855.997-239.009-183.897-1.799-48.555
Dec-0015.89157.363-231.893-177.4512.462-44.463
Jan-0121.54259.184-218.586-167.59610.170-37.226
Feb-0124.74059.732-204.687-157.98714.532-31.759
Mar-0125.94860.473-188.150-145.95715.974-25.094
Apr-0124.72061.640-171.681-134.24819.094-19.538
May-0131.63563.873-154.975-120.81026.220-10.158
Jun-0137.65366.094-143.452-110.23733.141-1.249
Jul-0140.88166.008-140.615-106.17935.0392.521
Aug-0142.05665.510-138.323-102.16635.6685.039
Sep-0139.15063.369-139.081-98.21234.8576.849
Oct-0135.61259.608-141.795-93.14130.8369.301
Nov-0132.82456.901-142.923-88.04330.03511.486
Dec-0134.44455.503-141.981-82.53231.57916.288
Jan-0232.73854.025-141.473-78.35931.22018.158
Feb-0228.70852.728-139.741-74.28429.60919.337
Mar-0230.12255.396-134.309-70.35834.36423.414
Apr-0233.02159.163-128.057-65.14540.27928.832
May-0233.20559.624-127.630-64.90040.87329.368
Jun-0233.23058.554-130.197-65.24239.91128.862
Jul-0233.52056.653-132.555-64.61238.41028.476
Aug-0231.68353.948-135.757-65.26234.69926.128
Sep-0224.89251.921-133.234-59.48434.13725.593
Oct-0223.44948.132-141.544-63.57928.89119.705
Nov-0224.58345.111-149.820-68.26625.05413.689
Dec-0224.12539.928-165.611-78.73716.1623.084
Jan-0323.82735.495-184.017-91.2914.921-6.428
Feb-0325.32031.495-198.484-101.026-4.412-14.243
Mar-0325.43130.270-204.821-104.453-7.206-16.305
Apr-0325.49028.075-216.879-111.051-12.016-20.884
May-0326.47623.048-237.579-121.921-20.680-27.635
Jun-0324.38319.099-257.273-132.403-30.655-35.479
Jul-0322.40418.909-267.382-136.177-35.231-38.901
Aug-0323.43521.639-269.115-134.051-33.314-36.460
Sep-0323.02220.157-286.886-141.546-39.162-40.473
Oct-0323.37021.117-295.860-143.207-40.325-40.165
Nov-0325.27425.832-289.530-136.962-34.143-34.019
Dec-0326.55628.914-287.446-133.495-31.891-30.585

Figure 10c. Trace Cumulative Squared Prediction Errors, 6-Month Forecast Horizon, 1994 - 2003: Forecast Combinations

Data for Figure 10c immediately follows.

Data for Figure 10c

MonthFC-MSPEFC-MSPE-XFC-MSPE-ALLFC-MCS-EW
Jan-94#N/A#N/A#N/A#N/A
Feb-94#N/A#N/A#N/A#N/A
Mar-94#N/A#N/A#N/A#N/A
Apr-94#N/A#N/A#N/A#N/A
May-94#N/A#N/A#N/A#N/A
Jun-9412.846-2.3164.779-6.089
Jul-9426.039-3.83710.123-10.020
Aug-9434.287-7.37011.967-14.904
Sep-9439.880-7.70814.379-12.138
Oct-9443.287-10.21214.505-11.307
Nov-9447.394-17.50112.116-15.583
Dec-9450.822-23.33810.260-18.203
Jan-9555.829-28.1619.935-20.148
Feb-9558.902-29.98610.565-20.568
Mar-9561.271-29.02912.360-19.058
Apr-9563.306-26.32815.047-17.070
May-9566.571-14.80923.821-11.286
Jun-9572.9422.61137.875-2.329
Jul-9572.40512.22644.0912.173
Aug-9569.10017.26246.1453.298
Sep-9565.06322.82948.2164.470
Oct-9559.72727.84949.3795.383
Nov-9553.44829.09448.0063.885
Dec-9546.66131.59447.2013.170
Jan-9638.34835.04646.1692.158
Feb-9634.45236.30946.0191.980
Mar-9633.32435.66946.3342.212
Apr-9635.08033.08847.1743.205
May-9641.44128.54949.5115.024
Jun-9647.63723.05950.6935.989
Jul-9656.95419.07454.1118.579
Aug-9661.99716.46155.8189.582
Sep-9662.72714.28155.8619.115
Oct-9661.28714.53156.1989.228
Nov-9659.04117.27657.28910.363
Dec-9657.79917.69357.61510.604
Jan-9756.27618.60358.11211.102
Feb-9755.03319.48258.67611.605
Mar-9755.70416.49258.02810.464
Apr-9757.28914.09858.18410.431
May-9759.73611.81358.86911.389
Jun-9759.80110.66058.83311.326
Jul-9758.06911.06158.78711.107
Aug-9757.13410.99058.86411.158
Sep-9755.15914.12160.19912.515
Oct-9753.01617.83362.02914.300
Nov-9751.73020.32263.61915.584
Dec-9749.70022.42964.54116.285
Jan-9846.45723.64364.63916.199
Feb-9844.04625.58265.20016.465
Mar-9842.77426.05565.61316.619
Apr-9841.20825.70865.63116.610
May-9839.12526.37265.84016.758
Jun-9836.95626.68065.90416.686
Jul-9836.25925.86265.96716.815
Aug-9831.68428.46566.27016.734
Sep-9823.80135.47767.55317.601
Oct-9817.87441.59969.07518.005
Nov-9813.56146.35370.59718.696
Dec-988.53151.63272.51820.799
Jan-993.88657.57775.01923.434
Feb-994.19156.20675.50923.776
Mar-998.45951.09675.83623.652
Apr-9913.06147.67277.09424.582
May-9918.15844.82278.74426.071
Jun-9923.65039.39679.15326.155
Jul-9930.13134.25780.10526.457
Aug-9932.37929.17778.95324.688
Sep-9935.08525.41978.77923.738
Oct-9938.06321.77678.68023.271
Nov-9940.00017.17477.43721.080
Dec-9942.25013.89276.93520.783
Jan-0044.74811.73677.03622.189
Feb-0046.7658.18376.21321.204
Mar-0049.1864.85475.69820.045
Apr-0050.9171.98575.07519.527
May-0051.230-0.26474.21318.746
Jun-0051.489-0.39974.42319.044
Jul-0051.9740.59475.35119.950
Aug-0051.8711.66676.02220.517
Sep-0051.4972.25376.41920.519
Oct-0052.7174.27878.30621.951
Nov-0057.11710.30084.06626.866
Dec-0055.83314.06785.81827.574
Jan-0151.11720.32887.50429.482
Feb-0144.96525.36387.72729.242
Mar-0137.62130.38587.35727.702
Apr-0131.32034.93187.19025.733
May-0126.02142.45289.56129.099
Jun-0123.01348.94192.53234.382
Jul-0117.37751.32691.64135.506
Aug-0112.84352.93490.53235.883
Sep-012.82752.84285.74232.927
Oct-01-11.22551.87178.45327.311
Nov-01-21.88151.83073.47424.588
Dec-01-31.45153.73870.39525.156
Jan-02-39.21454.34767.26324.234
Feb-02-46.56854.45264.01421.774
Mar-02-43.45457.86667.77625.420
Apr-02-39.14662.67972.64029.818
May-02-39.65463.21972.99630.354
Jun-02-43.19862.65971.25729.702
Jul-02-49.40162.05168.26428.647
Aug-02-56.64660.12363.84126.047
Sep-02-63.29159.82760.56724.001
Oct-02-72.87756.01753.75719.904
Nov-02-81.22852.95948.01717.360
Dec-02-92.63346.43938.57011.725
Jan-03-103.20139.92929.3906.502
Feb-03-113.21435.08421.6333.039
Mar-03-117.69634.08518.9122.582
Apr-03-123.48331.35014.3340.678
May-03-133.56325.4635.821-4.109
Jun-03-140.92519.480-1.651-8.565
Jul-03-142.22917.665-3.737-9.464
Aug-03-139.45820.380-1.088-6.740
Sep-03-142.84217.392-4.847-8.129
Oct-03-142.56817.858-4.735-7.138
Nov-03-137.09423.1160.914-2.692
Dec-03-133.87626.3064.098-0.704

Figure 11a. Trace Cumulative Squared Prediction Errors, 12-Month Forecast Horizon, 1994 - 2003: Yield-Only Models

Data for Figure 11a immediately follows.

Data for Figure 11a

MonthARVARNS2-ARNS2-VARNS1ATSM
Jan-94#N/A#N/A#N/A#N/A#N/A#N/A
Feb-94#N/A#N/A#N/A#N/A#N/A#N/A
Mar-94#N/A#N/A#N/A#N/A#N/A#N/A
Apr-94#N/A#N/A#N/A#N/A#N/A#N/A
May-94#N/A#N/A#N/A#N/A#N/A#N/A
Jun-94#N/A#N/A#N/A#N/A#N/A#N/A
Jul-94#N/A#N/A#N/A#N/A#N/A#N/A
Aug-94#N/A#N/A#N/A#N/A#N/A#N/A
Sep-94#N/A#N/A#N/A#N/A#N/A#N/A
Oct-94#N/A#N/A#N/A#N/A#N/A#N/A
Nov-94#N/A#N/A#N/A#N/A#N/A#N/A
Dec-9444.73978.40965.64841.34246.76042.104
Jan-9590.443158.376128.57783.89795.56085.763
Feb-95117.598197.621162.244107.653122.635110.421
Mar-95136.096222.214184.333122.797138.959126.268
Apr-95145.632233.662194.787132.451150.970136.396
May-95144.953231.116195.175138.725157.122142.448
Jun-95141.770227.249193.486145.166163.242148.582
Jul-95140.357221.969192.008148.588166.633151.624
Aug-95135.529211.112186.223148.307164.562150.713
Sep-95128.074202.190180.110150.080165.593151.686
Oct-95118.457192.741173.430151.995165.557152.618
Nov-95106.933182.283180.226154.021168.754151.877
Dec-9593.666171.499203.002158.188169.980152.498
Jan-9678.441147.771206.270148.658161.258140.080
Feb-9665.826121.378200.272134.892146.390124.672
Mar-9655.80199.044194.091122.804135.149111.196
Apr-9648.19179.977188.476112.384124.018100.105
May-9648.01870.777190.225110.416119.01097.937
Jun-9647.32060.024191.262107.885114.45095.228
Jul-9646.43750.257190.586105.379110.73792.453
Aug-9648.07645.836193.517106.571110.49493.479
Sep-9647.55735.861194.922104.614106.79191.222
Oct-9645.24619.406194.55399.63299.31085.719
Nov-9642.856-1.805193.34492.70190.06478.308
Dec-9647.385-5.363198.57297.45492.40082.954
Jan-9753.574-5.627206.540104.80498.18690.253
Feb-9755.864-10.903209.068106.72099.30892.004
Mar-9758.665-12.131212.448109.596101.45694.717
Apr-9757.582-19.231212.018108.49699.94893.249
May-9753.854-29.738209.664105.21597.02489.331
Jun-9750.316-41.021207.772102.00693.54285.460
Jul-9742.649-59.870203.00294.75987.31077.049
Aug-9736.537-74.176198.99189.49583.20770.806
Sep-9729.799-91.645194.23283.03577.49663.401
Oct-9723.629-112.673188.78375.07169.09954.545
Nov-9720.529-130.072186.84869.98963.29548.661
Dec-9714.080-150.440182.24262.80256.40740.301
Jan-984.416-176.930174.31452.01147.28228.068
Feb-98-4.195-199.846169.01143.18740.34717.636
Mar-98-14.106-220.703164.22535.17735.8717.748
Apr-98-23.976-242.797160.16226.43128.362-2.414
May-98-33.806-264.847156.73118.54520.085-11.846
Jun-98-43.327-289.349151.4638.90213.645-23.100
Jul-98-50.434-314.880147.827-1.2054.570-34.538
Aug-98-64.297-349.972141.063-16.264-7.636-51.839
Sep-98-83.999-399.261134.065-36.914-26.696-75.337
Oct-98-102.347-451.154127.194-60.319-49.469-101.300
Nov-98-118.377-497.090124.685-80.240-67.664-123.969
Dec-98-133.837-545.107120.647-101.995-89.067-148.151
Jan-99-147.688-593.920114.436-123.448-110.602-170.955
Feb-99-155.866-624.607112.964-135.667-122.586-184.576
Mar-99-165.441-657.357111.008-148.971-133.589-199.658
Apr-99-174.019-685.449110.618-158.655-143.906-210.838
May-99-178.479-704.079111.170-163.788-151.455-216.849
Jun-99-180.947-719.291112.094-167.250-155.689-220.965
Jul-99-182.394-730.837113.025-169.187-158.990-223.404
Aug-99-176.346-728.507118.003-161.498-152.913-215.505
Sep-99-163.146-711.414121.975-145.556-137.350-198.768
Oct-99-148.371-690.721133.412-127.343-119.252-180.040
Nov-99-134.052-669.578141.585-109.528-101.970-161.452
Dec-99-116.425-638.949148.029-88.609-81.863-139.128
Jan-00-94.515-597.537156.185-62.602-58.699-111.246
Feb-00-81.769-579.287159.901-49.902-48.752-97.588
Mar-00-68.837-563.346167.082-36.849-37.698-83.988
Apr-00-55.754-545.675173.963-23.959-26.190-70.295
May-00-47.952-537.168176.238-17.634-21.012-63.119
Jun-00-42.029-532.891177.848-12.382-15.410-57.483
Jul-00-36.111-528.082179.948-6.611-9.724-51.413
Aug-00-33.312-528.656180.401-3.078-5.307-48.000
Sep-00-30.357-529.420181.0860.468-1.040-44.581
Oct-00-28.644-531.265181.3253.7373.153-41.504
Nov-00-31.943-542.354180.7381.9602.373-44.208
Dec-00-40.137-560.598180.590-3.840-1.843-51.587
Jan-01-52.426-583.693186.548-12.331-4.885-62.859
Feb-01-65.722-611.048193.184-23.547-12.181-77.097
Mar-01-80.023-645.128206.202-39.052-22.755-95.694
Apr-01-93.480-671.016225.502-47.980-27.769-108.351
May-01-107.843-692.959250.138-51.710-38.022-115.836
Jun-01-121.004-722.291265.549-64.980-51.293-131.799
Jul-01-135.745-761.151279.021-87.024-72.336-155.663
Aug-01-151.430-805.937292.602-112.854-99.817-183.476
Sep-01-172.474-860.861303.384-145.844-141.579-217.271
Oct-01-195.785-926.777312.611-187.974-193.161-259.919
Nov-01-216.089-983.877322.360-222.262-238.121-293.726
Dec-01-234.893-1034.219326.131-248.153-274.462-319.020
Jan-02-255.852-1085.745312.557-270.466-303.958-341.242
Feb-02-276.883-1140.990296.552-294.140-292.936-364.453
Mar-02-291.529-1177.604286.087-305.383-306.948-375.817
Apr-02-312.902-1228.830259.311-324.307-330.538-395.566
May-02-334.662-1282.170228.908-342.604-350.249-415.224
Jun-02-359.544-1341.481194.747-364.008-374.205-437.562
Jul-02-386.027-1414.562146.938-391.714-405.845-465.189
Aug-02-413.498-1494.384100.668-419.250-440.141-492.778
Sep-02-439.608-1590.33336.091-445.617-475.258-517.969
Oct-02-458.852-1680.671-20.368-465.118-501.607-536.750
Nov-02-478.195-1757.791-72.069-479.753-518.383-551.998
Dec-02-504.537-1846.469-141.110-496.476-536.584-569.709
Jan-03-529.763-1929.778-201.462-512.501-554.587-586.829
Feb-03-555.960-2019.713-264.548-529.987-574.471-605.083
Mar-03-586.166-2099.561-318.804-542.030-584.962-619.397
Apr-03-613.229-2185.047-381.952-558.429-600.321-637.202
May-03-642.937-2279.814-450.794-576.743-618.480-656.220
Jun-03-670.828-2378.615-525.239-597.712-641.149-677.441
Jul-03-686.291-2454.235-584.692-612.416-662.748-691.418
Aug-03-696.974-2519.582-621.762-621.010-677.341-699.944
Sep-03-707.738-2601.291-658.902-630.614-693.665-708.745
Oct-03-714.947-2666.408-695.750-635.955-704.490-713.528
Nov-03-723.684-2729.439-731.290-642.467-714.460-720.088
Dec-03-728.839-2791.349-761.748-645.526-721.612-722.951

Figure 11b. Trace Cumulative Squared Prediction Errors, 12-Month Forecast Horizon, 1994 - 2003: Macro Models

Data for Figure 11b immediately follows.

Data for Figure 11b

MonthAR-XVAR-XNS2-AR-XNS2-VAR-XNS1-XATSM-X
Jan-94#N/A#N/A#N/A#N/A#N/A#N/A
Feb-94#N/A#N/A#N/A#N/A#N/A#N/A
Mar-94#N/A#N/A#N/A#N/A#N/A#N/A
Apr-94#N/A#N/A#N/A#N/A#N/A#N/A
May-94#N/A#N/A#N/A#N/A#N/A#N/A
Jun-94#N/A#N/A#N/A#N/A#N/A#N/A
Jul-94#N/A#N/A#N/A#N/A#N/A#N/A
Aug-94#N/A#N/A#N/A#N/A#N/A#N/A
Sep-94#N/A#N/A#N/A#N/A#N/A#N/A
Oct-94#N/A#N/A#N/A#N/A#N/A#N/A
Nov-94#N/A#N/A#N/A#N/A#N/A#N/A
Dec-94-16.16214.816-8.777-35.258-5.360-13.122
Jan-95-22.16830.565-17.809-70.958-4.530-24.699
Feb-95-28.41937.599-32.388-101.541-10.178-39.433
Mar-95-19.68543.190-32.618-113.782-6.881-38.255
Apr-95-13.46746.064-36.724-123.780-6.018-38.894
May-95-9.84948.209-35.923-124.533-1.257-37.219
Jun-95-4.32350.795-29.109-118.7838.215-30.116
Jul-95-2.08052.095-29.109-120.94010.644-30.570
Aug-950.87952.751-26.952-119.62214.958-27.983
Sep-954.97354.526-17.262-109.06226.670-17.200
Oct-9510.99857.042-2.606-92.03843.319-0.604
Nov-9521.80563.72030.378-59.67075.11729.111
Dec-9536.17475.45278.922-12.013119.15173.029
Jan-9655.91781.820118.00225.353156.610108.046
Feb-9664.61883.667132.31339.826171.426122.294
Mar-9671.92784.795138.79246.913180.617130.329
Apr-9675.64985.442135.94045.528183.653132.522
May-9673.34686.616116.91330.090181.329126.291
Jun-9671.44487.39894.28611.323177.370119.751
Jul-9668.43587.88075.258-5.882171.032110.815
Aug-9665.98088.61550.827-26.170163.698102.285
Sep-9663.78389.17525.225-45.648157.56294.102
Oct-9661.30789.6021.030-63.810152.30385.411
Nov-9655.63590.238-24.599-83.230144.64874.421
Dec-9651.68991.498-67.671-118.121138.19061.999
Jan-9745.04693.957-97.711-144.912130.75351.117
Feb-9742.72394.865-113.631-160.230125.64945.496
Mar-9737.76395.225-139.829-182.440113.30734.990
Apr-9734.18395.060-157.482-198.188102.84126.336
May-9734.36895.086-165.800-204.95599.38023.904
Jun-9734.09495.068-174.735-212.47895.62019.970
Jul-9736.86595.301-175.487-212.20597.99321.424
Aug-9738.82495.492-178.145-213.84898.19221.252
Sep-9740.47295.566-181.684-216.58697.87520.577
Oct-9741.30195.195-187.650-221.39197.12018.323
Nov-9741.17095.001-201.472-231.85594.57514.797
Dec-9742.43194.646-205.596-235.11295.01013.806
Jan-9845.45194.094-203.868-233.08698.89815.651
Feb-9848.16893.931-203.045-231.720102.51317.778
Mar-9852.48894.414-195.726-224.224111.41224.230
Apr-9858.12295.173-192.039-219.736117.89929.062
May-9863.71696.130-191.050-217.318123.52533.051
Jun-9868.06196.205-192.170-216.609127.91336.779
Jul-9869.38695.953-205.447-224.982125.71333.724
Aug-9873.93395.947-197.089-216.040135.70341.768
Sep-9881.69996.236-178.109-198.094151.57156.553
Oct-9890.28995.835-164.167-184.439164.43467.097
Nov-9895.29195.738-153.623-173.361175.46675.645
Dec-98100.90495.233-145.296-164.116184.85183.948
Jan-99104.07493.839-142.614-159.609189.53187.062
Feb-99105.41293.712-153.053-162.994190.75488.105
Mar-99107.77593.480-158.405-162.826193.41790.896
Apr-99108.46593.446-167.125-165.113195.34692.481
May-99107.86193.639-186.494-174.815193.71590.390
Jun-99103.73194.035-212.401-189.334183.80281.847
Jul-9998.25294.337-241.963-207.087172.61171.011
Aug-9991.12896.423-278.894-231.302162.40659.525
Sep-9980.291100.419-338.910-276.081143.60034.850
Oct-9970.666105.151-385.980-312.272131.03616.829
Nov-9968.533109.599-438.289-347.178123.2577.345
Dec-9961.599114.050-504.920-391.458107.460-10.949
Jan-0055.165119.837-573.677-435.80886.084-25.770
Feb-0044.632120.930-622.412-469.64058.013-46.000
Mar-0034.615122.712-660.953-497.15034.734-61.983
Apr-0028.907124.533-697.837-523.46318.197-75.784
May-0020.997124.637-728.206-546.6951.205-90.484
Jun-0020.531124.951-749.884-561.867-5.587-97.059
Jul-0025.143125.865-764.591-571.408-7.457-97.222
Aug-0024.734126.064-778.781-580.585-11.514-102.354
Sep-0023.641126.338-791.689-588.870-16.426-107.655
Oct-0023.884126.719-802.568-595.605-17.859-109.575
Nov-0024.814126.887-806.634-597.093-17.157-109.285
Dec-0027.482127.287-799.772-590.650-10.751-104.010
Jan-0130.949128.712-780.327-574.8314.265-92.471
Feb-0132.982129.778-759.986-559.13315.705-83.784
Mar-0140.162131.694-732.555-537.79531.988-71.332
Apr-0141.796135.134-703.906-514.37848.747-57.572
May-0144.729140.695-669.725-484.18464.324-37.174
Jun-0148.224143.025-639.704-459.57277.404-22.953
Jul-0163.060145.417-601.837-429.020100.2730.597
Aug-0172.800146.925-560.878-397.820116.50618.774
Sep-0180.641148.255-504.263-354.211128.37340.476
Oct-0183.690148.198-444.763-312.856138.76756.455
Nov-01105.104150.401-387.622-267.899163.51885.829
Dec-01125.071152.960-343.684-229.954187.451114.563
Jan-02135.882152.720-321.941-207.532200.200132.025
Feb-02140.350151.590-302.827-187.191207.014143.611
Mar-02139.947151.908-290.874-174.128212.496152.009
Apr-02136.804148.815-285.111-164.087210.518154.755
May-02133.587145.094-281.720-155.596209.184156.041
Jun-02135.962141.190-276.640-144.602211.628162.117
Jul-02129.740134.544-279.029-140.124201.156155.662
Aug-02119.135127.071-280.179-135.970185.738146.828
Sep-02109.366116.744-304.194-144.644162.913132.744
Oct-0288.498107.814-331.670-158.465126.370105.570
Nov-0283.807101.043-345.150-162.503113.92296.176
Dec-0281.07691.923-365.510-169.185103.36987.773
Jan-0379.61283.982-377.149-172.65195.48181.162
Feb-0372.12574.400-393.139-182.43280.13166.717
Mar-0358.33666.294-406.078-190.74967.26550.278
Apr-0350.42256.531-436.034-212.96250.06628.656
May-0346.46645.315-474.501-241.61532.6435.659
Jun-0338.08932.851-522.456-278.2597.059-22.675
Jul-0333.25826.146-560.336-305.445-12.800-38.925
Aug-0331.96123.287-579.754-318.707-20.389-44.665
Sep-0330.66119.667-597.382-330.802-27.824-50.167
Oct-0329.14118.399-615.511-340.375-32.613-53.607
Nov-0327.89715.618-636.789-351.092-38.385-57.494
Dec-0324.95015.066-659.037-361.419-47.134-63.207

Figure 11c. Trace Cumulative Squared Prediction Errors, 12-Month Forecast Horizon, 1994 - 2003: Forecast Combinations

Data for Figure 11c immediately follows.

Notes: Figures 10 and 11 show the Trace Cumulative Squared Prediction Error, relative to the random walk, of individual yield-only models in Panel (a), individual models with macro factors in Panel (b) and of forecast combinations schemes in Panel (c). Figure 10 shows TCSPEs for a 6-month forecast horizon whereas Figure 11 does so for a 12-month horizon. The forecast sample is 1994:1 - 2003:12.

Data for Figure 11c

MonthFC-MSPEFC-MSPE-XFC-MSPE-ALLFC-MCS-EW
Jan-94#N/A#N/A#N/A#N/A
Feb-94#N/A#N/A#N/A#N/A
Mar-94#N/A#N/A#N/A#N/A
Apr-94#N/A#N/A#N/A#N/A
May-94#N/A#N/A#N/A#N/A
Jun-94#N/A#N/A#N/A#N/A
Jul-94#N/A#N/A#N/A#N/A
Aug-94#N/A#N/A#N/A#N/A
Sep-94#N/A#N/A#N/A#N/A
Oct-94#N/A#N/A#N/A#N/A
Nov-94#N/A#N/A#N/A#N/A
Dec-9441.195-10.20411.458-20.504
Jan-9583.216-17.43025.124-33.768
Feb-95106.869-26.51630.029-45.241
Mar-95122.432-24.86437.910-41.124
Apr-95131.863-24.37842.699-39.362
May-95135.575-21.53347.404-36.658
Jun-95138.703-15.04553.994-31.162
Jul-95140.512-13.56257.029-30.193
Aug-95138.848-10.76759.403-28.305
Sep-95137.730-3.07664.550-22.716
Oct-95135.9448.08271.498-16.211
Nov-95135.03930.30186.243-1.221
Dec-95136.42364.014109.80623.081
Jan-96127.75191.493125.12537.930
Feb-96116.334103.393129.68842.031
Mar-96106.757111.598133.26145.029
Apr-9698.821115.409135.41047.081
May-9698.616112.460137.94749.795
Jun-9697.834108.568139.46451.394
Jul-9696.681103.869140.13551.865
Aug-9698.69398.246141.50953.468
Sep-9698.24093.331142.58254.741
Oct-9695.32388.731143.14755.109
Nov-9691.43582.923143.74055.666
Dec-9696.72873.363145.34257.293
Jan-97104.28165.111148.56360.954
Feb-97106.71560.626149.86662.177
Mar-97109.79552.341149.63962.007
Apr-97109.10546.496148.79661.058
May-97106.37945.323148.86261.090
Jun-97103.68043.511148.84660.565
Jul-9797.38845.972149.64160.531
Aug-9792.77847.337150.55160.979
Sep-9787.20748.290151.13661.093
Oct-9780.71447.954150.38459.776
Nov-9777.07245.736149.83158.851
Dec-9770.96146.167149.18657.555
Jan-9861.80048.964148.47656.827
Feb-9854.27551.829148.52656.919
Mar-9847.19658.111150.46058.948
Apr-9839.61363.905152.85961.560
May-9832.32269.329155.45363.956
Jun-9824.32373.613156.79165.125
Jul-9816.79573.282156.52564.895
Aug-984.39781.085157.58666.744
Sep-98-12.96793.875159.73070.307
Oct-98-31.334104.346160.56572.733
Nov-98-46.542113.068161.33574.742
Dec-98-62.816121.080161.56076.173
Jan-99-78.582125.642159.70375.522
Feb-99-86.990127.464160.29276.699
Mar-99-96.246130.697161.18677.977
Apr-99-103.466132.719161.61978.639
May-99-106.836131.367161.99178.799
Jun-99-108.412126.248162.19678.579
Jul-99-108.915119.600161.94977.577
Aug-99-101.336110.791163.82778.343
Sep-99-86.24693.890164.90476.872
Oct-99-69.36980.925168.46078.318
Nov-99-53.36070.992172.58580.978
Dec-99-34.74555.088174.45781.023
Jan-00-12.29138.610177.34680.766
Feb-00-1.20621.988174.67575.149
Mar-0010.1968.446173.82170.872
Apr-0021.691-2.901174.00269.074
May-0027.820-13.950171.84064.433
Jun-0032.641-19.236171.94763.170
Jul-0037.590-20.457174.04464.719
Aug-0040.366-23.599174.41063.680
Sep-0043.225-26.864174.74562.661
Oct-0045.574-28.369175.72162.534
Nov-0043.746-27.811176.07662.527
Dec-0038.620-23.315177.01863.779
Jan-0132.408-13.758180.42966.710
Feb-0124.255-5.496182.00966.994
Mar-0114.7086.742185.73468.604
Apr-019.76218.983191.35871.392
May-017.20535.041200.53976.629
Jun-01-0.86047.249204.91677.746
Jul-01-14.07365.555210.89981.694
Aug-01-29.79981.581214.09881.392
Sep-01-51.726100.191215.76178.362
Oct-01-79.263116.303212.87070.252
Nov-01-101.399140.332218.18573.054
Dec-01-119.223161.761224.28678.052
Jan-02-138.000173.405223.94780.321
Feb-02-151.872181.631222.98378.453
Mar-02-162.208186.836222.12877.723
Apr-02-181.233187.965214.59371.995
May-02-200.296188.441206.65466.370
Jun-02-222.462191.576199.20362.059
Jul-02-250.179187.641184.22949.232
Aug-02-278.819182.020167.72835.522
Sep-02-309.468170.113146.10515.984
Oct-02-333.287153.000123.672-5.078
Nov-02-353.376146.345110.451-16.191
Dec-02-378.966138.81294.190-29.970
Jan-03-402.885133.60880.378-41.746
Feb-03-428.501123.68462.427-57.280
Mar-03-450.539113.74445.869-70.554
Apr-03-475.13399.46725.364-88.332
May-03-502.55083.7142.634-107.851
Jun-03-531.63863.364-23.969-131.969
Jul-03-551.16450.720-41.522-147.143
Aug-03-563.46046.151-50.260-154.098
Sep-03-576.65941.808-59.205-160.225
Oct-03-585.44639.132-65.265-164.276
Nov-03-595.60434.934-72.792-169.694
Dec-03-601.75130.964-78.949-174.332

Figure 12a. Observed and Predicted Yields, 1-Month Forecast Horizon: 3-Month Yield

Data for Figure 12a immediately follows.

Data for Figure 12a

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-943.0163.0713.1333.2853.1143.096
Feb-943.4313.0733.0773.1713.0072.965
Mar-943.5363.4343.4213.5553.4233.418
Apr-943.9453.6263.7373.7583.6533.648
May-944.2704.1254.1774.1094.0404.020
Jun-944.2234.2644.2514.3784.2834.296
Jul-944.3534.2554.2804.3714.2834.275
Aug-944.6444.3784.3924.4804.3734.370
Sep-944.7764.6554.6904.7654.6614.680
Oct-945.1384.8524.9614.9634.8844.890
Nov-945.6655.1995.1575.1635.1455.166
Dec-945.6625.6695.6495.6885.6535.713
Jan-955.9325.6765.5895.6625.6285.728
Feb-955.8685.8785.8245.9135.8415.923
Mar-955.8235.8685.7815.8205.7595.825
Apr-955.8095.8105.8615.9015.7795.846
May-955.7425.7345.7575.8675.7285.801
Jun-955.5515.7445.6705.7265.6275.693
Jul-955.5275.5565.4255.4875.4305.479
Aug-955.3985.5485.4985.5295.4175.471
Sep-955.3535.4375.4155.4405.3445.397
Oct-955.4215.4045.4035.4215.3005.365
Nov-955.4245.4235.2695.3495.2695.333
Dec-955.0595.3505.2755.4195.2635.354
Jan-965.0005.0124.7674.9254.8704.931
Feb-964.9825.0514.9454.9904.8934.942
Mar-965.0994.9584.9535.0494.9074.963
Apr-965.1005.1345.1755.1875.0625.121
May-965.1385.0855.0225.0894.9935.055
Jun-965.1445.2215.2335.1845.0985.144
Jul-965.2795.2195.1395.1185.0745.114
Aug-965.2495.2775.2285.2785.2015.258
Sep-965.0575.2445.2525.2955.1905.250
Oct-965.1165.0205.0585.1475.0165.079
Nov-965.0985.0965.0475.1275.0265.084
Dec-965.1205.1155.0405.0925.0335.077
Jan-975.1255.1965.1205.0935.0735.108
Feb-975.1965.1325.0975.1345.0575.108
Mar-975.2865.2275.1985.1955.1495.188
Apr-975.2565.3045.3425.3495.2805.331
May-975.1405.2525.2045.2515.1885.232
Jun-975.1945.0654.9915.1125.0455.100
Jul-975.2035.1945.1375.1765.0895.153
Aug-975.1855.1895.1345.1905.1135.167
Sep-975.0205.2225.1705.1775.1265.174
Oct-975.1735.1005.0124.9914.9555.006
Nov-975.2575.1745.0275.0795.0345.098
Dec-975.3075.3025.1635.1655.1395.195
Jan-985.1585.3515.2235.2255.1975.248
Feb-985.2745.1285.0075.1075.0485.097
Mar-985.1345.2875.1565.1935.1555.209
Apr-984.9465.1125.1005.1595.0615.120
May-984.9974.9494.8674.9324.8894.944
Jun-985.0125.0364.8734.9034.9304.979
Jul-985.0494.9854.9625.0264.9435.005
Aug-984.8464.9284.8014.9604.8854.957
Sep-984.3024.7894.6884.8024.7204.778
Oct-984.3234.3074.1674.2424.2074.263
Nov-984.4904.2744.0824.2134.1544.209
Dec-984.4354.5134.4414.4784.4364.482
Jan-994.4374.4414.3734.4114.3644.419
Feb-994.6424.4394.3544.3994.3184.380
Mar-994.4534.6864.6044.5814.5454.611
Apr-994.5184.4024.4144.4924.3684.426
May-994.6204.5324.4904.5014.4514.509
Jun-994.7344.5934.5294.5554.5294.581
Jul-994.7134.7244.6544.6684.6544.713
Aug-994.9064.8174.7344.6344.6784.711
Sep-994.8074.9674.8624.8064.8534.902
Oct-995.0454.7504.6634.7364.6924.751
Nov-995.2495.0584.8414.8354.9204.972
Dec-995.3275.2295.1435.1735.1935.235
Jan-005.6635.3645.3785.3595.3555.388
Feb-005.7355.7305.6895.6015.6465.730
Mar-005.8275.7585.7335.6835.7235.758
Apr-005.8005.8255.8975.8455.8445.825
May-005.5755.8125.7515.6725.7585.807
Jun-005.8395.5865.3795.3335.5135.586
Jul-006.1945.8125.8145.7885.8285.869
Aug-006.2566.2056.1976.1306.1466.205
Sep-006.1666.1486.0996.1596.1386.195
Oct-006.3086.1426.0396.0446.0736.142
Nov-006.1626.3306.2506.2066.2416.281
Dec-005.8496.1466.0656.0636.0736.116
Jan-014.9665.7415.6115.7025.6765.741
Feb-014.8334.8824.7604.8504.7914.882
Mar-014.2664.7854.7714.8314.7344.785
Apr-013.8534.2854.2974.3014.2014.235
May-013.6053.8203.8183.8953.8133.843
Jun-013.6283.6043.5673.5913.5213.562
Jul-013.5213.6093.5703.6323.5433.569
Aug-013.3353.4553.4753.6123.4253.466
Sep-012.3493.3733.3593.4043.2773.305
Oct-012.0272.4072.4342.5172.3402.356
Nov-011.7822.0262.0032.1591.9982.011
Dec-011.6981.7101.7181.9061.7021.744
Jan-021.7591.5771.6141.8161.5931.648
Feb-021.7571.6881.7391.9081.6911.746
Mar-021.7851.7101.7421.9091.6841.740
Apr-021.7491.8291.9331.9881.8461.895
May-021.7221.7471.8001.9041.7291.774
Jun-021.6891.6561.7141.9051.6961.741
Jul-021.6931.6031.6031.8291.6041.646
Aug-021.6671.6701.6411.8731.6541.662
Sep-021.5431.5861.5551.8401.5981.619
Oct-021.4361.4211.3781.7141.4591.479
Nov-021.2191.3811.3471.6241.3941.395
Dec-021.1871.2001.2451.4341.2131.225
Jan-031.1691.1811.1611.3751.1841.176
Feb-031.2051.2661.2581.3681.2471.218
Mar-031.1041.3071.2891.3951.2731.247
Apr-031.1111.0861.1081.3231.1471.126
May-031.1101.0711.0801.3161.1671.140
Jun-030.8761.0111.0051.3201.1131.102
Jul-030.9400.9780.9651.0870.9710.946
Aug-030.9881.0661.1051.1921.0531.021
Sep-030.9281.0841.1281.2131.0801.058
Oct-030.9371.0060.9921.1381.0020.972
Nov-030.9261.0851.1161.1641.0651.038
Dec-030.9281.0221.0761.1551.0251.017

Figure 12b. Observed and Predicted Yields, 1-Month Forecast Horizon: 2-Year Yield

Data for Figure 12b immediately follows.

Data for Figure 12b

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-944.0794.1994.1454.3834.1654.203
Feb-944.6394.1064.0594.2744.0424.093
Mar-945.1704.6224.5614.8134.5704.631
Apr-945.6805.2135.1525.3155.1265.206
May-945.9285.7875.6615.7555.6025.735
Jun-946.0875.8985.7275.9835.7805.935
Jul-945.9076.0885.8996.1035.9356.103
Aug-946.0865.9055.7535.9695.7915.923
Sep-946.4976.0785.9046.1015.9546.099
Oct-946.7326.5336.3826.5016.4166.522
Nov-947.2636.7586.5996.7196.6396.752
Dec-947.5037.2456.9997.1937.0817.265
Jan-957.1267.4877.1387.3837.2487.503
Feb-956.6687.0666.8487.0776.9627.114
Mar-956.6726.6556.5076.6666.5486.675
Apr-956.4696.6486.5046.6696.5486.676
May-955.7806.3986.2816.5096.3626.458
Jun-955.7085.7715.7215.8955.7265.794
Jul-955.7925.7015.5995.8035.6345.723
Aug-955.7565.7945.7385.8985.7335.810
Sep-955.7255.7765.6735.8365.6815.780
Oct-955.5335.7485.6345.8065.6445.750
Nov-955.2735.5265.4455.6505.4625.549
Dec-955.0885.2155.1695.4325.2105.273
Jan-964.8705.0514.9465.2245.0105.096
Feb-965.3634.9004.9025.0724.8704.885
Mar-965.6915.3495.2415.4635.2825.356
Apr-965.9405.7115.5825.7585.6025.715
May-966.1615.9165.7575.9765.8075.947
Jun-966.0136.2126.0276.1516.0406.192
Jul-966.1176.0565.9096.0425.9086.043
Aug-966.2316.1065.9726.1486.0116.127
Sep-966.0086.2116.0696.2546.1146.237
Oct-965.6685.9655.8216.0315.8856.008
Nov-965.5085.6465.5535.7395.5865.677
Dec-965.7905.5135.4015.5765.4395.527
Jan-975.8395.8385.7245.8325.7185.822
Feb-976.0085.8365.7055.8685.7455.853
Mar-976.3356.0205.8555.9875.8876.026
Apr-976.1936.3296.1676.3076.2066.345
May-976.1176.1696.0086.1756.0576.198
Jun-975.9916.0395.8746.0935.9526.103
Jul-975.6605.9705.8135.9845.8665.998
Aug-975.8745.6355.4945.6715.5385.648
Sep-975.7125.8875.7655.9015.7935.893
Oct-975.5675.7555.6205.7235.6185.734
Nov-975.7115.5605.3975.5795.4565.581
Dec-975.5785.7355.5555.6965.6025.735
Jan-985.2635.6005.4635.5825.4805.602
Feb-985.4695.2315.1165.3165.1735.247
Mar-985.5035.4655.3265.4795.3665.484
Apr-985.5095.4725.3225.5075.3875.509
May-985.4655.4995.3215.5005.3975.522
Jun-985.4045.4855.3285.4655.3735.488
Jul-985.4185.3755.2365.4135.2875.411
Aug-984.8145.3205.1865.4235.2775.368
Sep-984.2774.7734.7424.9314.7674.793
Oct-984.1674.2794.2384.3994.2414.279
Nov-984.4784.1274.1784.3724.1754.127
Dec-984.5194.4914.4524.5974.4494.485
Jan-994.5314.5194.4404.6064.4594.519
Feb-995.0974.5324.3924.5854.4434.531
Mar-994.9385.1244.9865.1135.0065.111
Apr-995.0114.8944.7744.9834.8444.916
May-995.3545.0144.8965.0364.9275.012
Jun-995.4565.3285.1755.3445.2405.341
Jul-995.5595.4455.3075.4425.3525.450
Aug-995.6505.6255.4925.5365.4865.592
Sep-995.5505.6855.6075.6695.5945.668
Oct-995.7235.5005.3945.5735.4545.525
Nov-995.9315.7295.6235.7265.6675.726
Dec-996.1485.9125.7945.9155.8595.921
Jan-006.5066.1666.0556.1386.0946.157
Feb-006.4416.5456.3716.4236.4246.526
Mar-006.3906.4496.2976.3696.3666.453
Apr-006.5676.3826.1936.2726.2856.386
May-006.5976.5726.3516.4146.4506.577
Jun-006.2806.5826.3296.4326.4656.600
Jul-006.2046.2496.1456.2276.1996.264
Aug-006.0876.2136.2056.2286.1976.218
Sep-005.8856.0135.9476.0786.0246.049
Oct-005.8245.8715.9065.9775.9025.878
Nov-005.5485.8565.9285.9525.8785.840
Dec-005.0515.5535.6085.6765.5875.551
Jan-014.5674.9935.0975.2385.1015.022
Feb-014.3864.5184.6304.7744.6204.542
Mar-014.1864.3704.4874.6134.4594.370
Apr-014.2784.2134.3054.3954.2614.213
May-014.2134.2554.3514.4924.3274.255
Jun-014.2334.2144.2724.3974.2444.214
Jul-013.7744.2254.3064.4554.2694.225
Aug-013.6093.7423.8684.0643.8493.742
Sep-012.8223.6513.7743.8933.6973.651
Oct-012.3702.8813.1073.2172.9842.852
Nov-012.8402.3942.5772.7692.5132.382
Dec-013.0662.7942.8343.1172.8752.817
Jan-023.1532.9963.0023.2873.0473.030
Feb-023.0443.1163.1023.3603.1313.134
Mar-023.6743.0292.9973.2473.0103.036
Apr-023.2163.7183.6143.8143.6413.696
May-023.1873.2373.1903.4023.1883.227
Jun-022.8753.1623.0663.3453.1553.175
Jul-022.2232.8392.7983.0672.8722.857
Aug-022.1092.2332.4322.6012.3592.228
Sep-021.6812.0762.2052.4432.2222.092
Oct-021.6651.6151.7302.0301.7701.648
Nov-022.0391.6431.8422.0581.8301.654
Dec-021.5822.0382.1782.3732.1652.038
Jan-031.6911.5961.7661.9391.7311.589
Feb-031.5101.7811.9782.0561.8911.736
Mar-031.4861.6031.7951.8621.7171.557
Apr-031.4771.4911.7021.8561.6731.489
May-031.3171.4651.6961.8591.6491.471
Jun-031.2991.2651.3771.6291.4211.291
Jul-031.7381.3921.5411.6271.4641.346
Aug-031.9611.8432.0772.1121.9441.791
Sep-031.4622.0402.1862.2572.0962.001
Oct-031.8211.5391.7111.7981.6381.501
Nov-032.0341.9422.0772.1221.9921.882
Dec-031.8392.1102.1762.2802.1492.073

Figure 12c. Observed and Predicted Yields, 1-Month Forecast Horizon: 5-Year Yield

Data for Figure 12c immediately follows.

Data for Figure 12c

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-945.0185.1875.2005.4255.2125.198
Feb-945.5875.0155.0575.2655.0624.999
Mar-946.2065.5535.5495.7875.5815.568
Apr-946.5926.2146.1996.3786.2086.187
May-946.7236.6456.5526.6906.5506.566
Jun-946.9216.6836.5766.8226.6556.664
Jul-946.6726.9056.7696.9916.8296.875
Aug-946.7546.6546.5596.7846.6266.648
Sep-947.2186.7356.6526.8626.7046.735
Oct-947.4127.2317.1077.2817.1637.187
Nov-947.6737.4197.2897.4697.3527.381
Dec-947.6747.6517.4527.6607.5507.630
Jan-957.4197.6527.4247.6607.5237.631
Feb-956.9617.3667.1937.4247.2987.379
Mar-956.9736.9426.8417.0346.9076.961
Apr-956.7676.9466.8507.0446.9106.970
May-955.9936.7056.6616.8826.7176.768
Jun-955.8945.9735.9986.1676.0076.020
Jul-956.0765.8755.9196.0935.9265.924
Aug-955.9856.0636.1316.2946.1186.118
Sep-955.9125.9896.0056.1606.0286.012
Oct-955.7265.9145.9216.0745.9125.929
Nov-955.4565.7075.7195.9015.7255.745
Dec-955.3075.4035.4345.6495.4655.474
Jan-965.1905.2695.2435.4565.2925.310
Feb-965.6675.1945.2725.4215.2565.192
Mar-966.0435.6565.7325.9045.7245.710
Apr-966.3206.0496.0406.1906.0476.050
May-966.5626.2966.2666.4606.3046.309
Jun-966.3796.5936.5156.6446.5296.547
Jul-966.4936.4026.3576.4996.3686.376
Aug-966.6366.4796.3996.5776.4476.466
Sep-966.3866.6126.5466.7296.5936.607
Oct-966.0076.3476.2886.4936.3516.359
Nov-965.7565.9825.9596.1446.0146.006
Dec-966.1435.7485.7245.8865.7645.758
Jan-976.1826.1686.0956.2286.1316.126
Feb-976.3186.1746.1166.2866.1716.167
Mar-976.6746.3186.2176.3756.2706.284
Apr-976.4926.6606.5656.7306.6256.635
May-976.4126.4626.3716.5616.4406.450
Jun-976.3086.3436.2456.4836.3366.356
Jul-975.8326.2776.1786.3606.2276.256
Aug-976.1305.8005.7385.9205.8025.804
Sep-975.9116.1276.0676.2206.0896.107
Oct-975.6335.9285.8676.0035.8825.895
Nov-975.7595.6185.6055.7805.6435.645
Dec-975.6325.7675.6845.8325.7275.737
Jan-985.3105.6335.5545.6965.5865.601
Feb-985.5125.2695.2665.4445.3025.315
Mar-985.5445.4905.4345.5855.4645.481
Apr-985.5625.5055.4675.6385.5045.521
May-985.4855.5405.4825.6415.5245.537
Jun-985.3855.4875.4225.5585.4505.470
Jul-985.4675.3535.2965.4715.3385.357
Aug-984.8655.3875.2755.5025.3645.389
Sep-984.3474.8264.8325.0094.8634.878
Oct-984.4804.3354.2534.4204.2994.313
Nov-984.5624.4324.3644.5534.4264.442
Dec-984.5914.5554.5714.6974.5564.581
Jan-994.5274.5754.5504.6824.5564.581
Feb-995.2064.5154.5324.6664.5434.544
Mar-995.1695.2175.1795.3025.1805.195
Apr-995.2665.1275.0865.2625.1285.139
May-995.6405.2565.1775.3125.2075.215
Jun-995.7595.6175.4785.6375.5515.561
Jul-995.9225.7475.6065.7475.6765.687
Aug-995.9685.9585.8195.8935.8515.853
Sep-995.8795.9835.8745.9755.9115.915
Oct-996.0455.8355.7115.8795.8135.818
Nov-996.1436.0455.8755.9965.9455.955
Dec-996.3906.1276.0036.1346.0696.082
Jan-006.6606.3996.2736.3746.3256.338
Feb-006.5696.6866.5066.5856.5686.582
Mar-006.2536.5726.3836.4726.4696.578
Apr-006.4566.2506.0976.1876.1806.189
May-006.4536.4686.2406.3326.3416.361
Jun-006.1586.4406.2246.3456.3376.457
Jul-006.1346.1316.0226.1226.1016.114
Aug-005.9326.1436.0316.0976.0926.096
Sep-005.7975.8795.7735.8925.8695.893
Oct-005.7065.7835.7955.8645.8145.833
Nov-005.3895.7325.7715.8055.7525.772
Dec-004.9895.3965.4465.5075.4395.448
Jan-014.8474.9515.0315.1555.0524.970
Feb-014.6994.8124.8655.0134.8944.830
Mar-014.6204.6934.7334.8484.7524.696
Apr-014.9384.6434.6974.7944.6964.632
May-014.9774.9174.9655.1144.9774.928
Jun-015.0674.9754.9955.1305.0034.976
Jul-014.6715.0645.0255.1705.0535.065
Aug-014.4974.6504.6554.7984.6854.660
Sep-014.0554.5244.5294.6104.5134.510
Oct-013.6754.0954.1304.2264.1084.075
Nov-014.1033.6903.7453.8503.7123.683
Dec-014.4474.0614.1704.3464.1704.082
Jan-024.5194.3934.4254.6264.4544.420
Feb-024.3584.4904.4584.6264.4864.504
Mar-025.0034.3434.3284.4724.3374.350
Apr-024.5845.0304.9325.0404.9385.017
May-024.4144.5984.5554.6714.5624.546
Jun-024.1494.3994.4224.5794.4364.406
Jul-023.6364.1204.1854.3424.2024.135
Aug-023.2843.6333.8113.9153.7663.634
Sep-022.6733.2523.4383.5873.4293.268
Oct-022.8762.6142.8893.0652.8612.644
Nov-023.3192.8463.1173.2713.0782.861
Dec-022.8093.3093.4643.6353.4593.314
Jan-033.0442.8093.0283.1702.9992.809
Feb-032.7263.0963.2603.3363.2103.070
Mar-032.8252.7812.9753.0452.9212.753
Apr-032.8872.8212.9843.1332.9962.823
May-032.3512.8703.0003.1563.0132.879
Jun-032.5012.3002.5382.7032.5252.325
Jul-033.3622.5532.7712.8242.6842.527
Aug-033.5133.4233.5853.6433.5193.392
Sep-032.8803.5573.6513.7393.6243.535
Oct-033.2962.9213.1063.1753.0642.888
Nov-033.3873.3683.5103.5563.4513.296
Dec-033.2643.4253.5293.6323.5143.406

Figure 12d. Observed and Predicted Yields, 1-Month Forecast Horizon: 10-Year Yield

Data for Figure 12d immediately follows.

Notes: The figure shows the observed yields for different maturities (the black solid lines), together with the 1-month forecast from selected models. The dotted lines show forecasts from three individual models: the (Vector) Autoregressive Model with macro factors, and the two-step Nelson-Siegel model (without macro factors). The solid lines are for two forecast combination (FC) schemes: combining models with macro factors using performance based MSPE-weights, and combining model forecasts with MSPE-based weights using only the forecasts from models which are in the Model Confidence Set $\displaystyle \widehat{M}_{0.25}^{\ast} $. Forecasts and observed yields are shown for the out-of-sample period 1994:1 - 2003:12. The forecast are constructed using an expanding estimation window. The out-of-sample period 1989:1 - 1993:12 is used to determine the initial FC weights, and after that an expanding sample is used to compute combination weights.

Data for Figure 12d

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-945.8506.0095.9266.0715.9525.993
Feb-946.2015.8385.7565.8655.7785.794
Mar-946.8736.1616.1796.3296.1846.216
Apr-947.1486.8726.7986.9206.8076.842
May-947.2347.1887.0167.0937.0547.090
Jun-947.4547.1937.0117.1517.0857.150
Jul-947.2817.4357.2157.3287.2907.370
Aug-947.2637.2597.0517.1217.0957.187
Sep-947.6787.2407.1317.1927.1387.209
Oct-947.8557.6847.5327.5747.5507.612
Nov-947.8567.8577.7077.7307.7177.803
Dec-947.7427.8327.6547.6797.6957.855
Jan-957.5607.7167.4507.4507.5037.741
Feb-957.1337.5067.4177.4267.4177.526
Mar-957.1997.1087.1657.1407.0847.151
Apr-957.1047.1677.2127.1777.1287.196
May-956.3297.0397.0377.0487.0217.076
Jun-956.2816.2996.3876.3676.3046.364
Jul-956.5446.2526.2846.2706.2156.294
Aug-956.3186.5216.5586.5536.4836.546
Sep-956.2026.3126.3726.3486.3036.350
Oct-956.0436.1926.2296.2136.1576.232
Nov-955.7186.0166.0346.0475.9826.068
Dec-955.5645.6595.8175.8425.7275.765
Jan-965.6055.5215.5255.5865.5195.564
Feb-966.1085.5955.6945.7145.6205.600
Mar-966.3236.0936.1696.1926.1156.127
Apr-966.6346.3226.4026.4266.3276.360
May-966.7876.6076.6276.6606.5886.649
Jun-966.6746.8116.8386.8316.7636.819
Jul-966.7496.6906.6716.6656.6216.684
Aug-966.9026.7346.7036.7316.6726.748
Sep-966.6786.8766.8786.9016.8396.904
Oct-966.3026.6386.6336.6736.6096.679
Nov-966.0146.2746.3116.3456.2946.332
Dec-966.3876.0006.0146.0385.9786.037
Jan-976.4806.4046.4056.3896.3506.400
Feb-976.4886.4696.4766.4676.4166.484
Mar-976.8276.4846.5256.5146.4646.507
Apr-976.6516.8106.8546.8556.8016.850
May-976.5936.6186.6426.6626.6066.661
Jun-976.4296.5256.5006.5736.5046.589
Jul-975.9626.3946.4576.4836.3946.452
Aug-976.2525.9265.9856.0165.9405.990
Sep-976.0356.2446.3036.3156.2406.287
Oct-975.7706.0436.0586.0606.0066.069
Nov-975.8085.7505.8405.8275.7605.776
Dec-975.6835.8105.8555.8125.7975.809
Jan-985.4915.6765.7285.7045.6465.680
Feb-985.5405.4455.4845.5035.4615.468
Mar-985.5745.5115.5845.6055.5285.526
Apr-985.6025.5325.6455.6635.5845.553
May-985.4615.5785.5795.6165.5845.590
Jun-985.3465.4585.4635.4925.4495.460
Jul-985.4195.3125.4035.4205.3585.329
Aug-985.0475.3425.3715.4505.3785.381
Sep-984.4435.0054.9965.0444.9865.026
Oct-984.6684.4224.3824.3984.3704.432
Nov-984.6644.6124.6084.6734.6094.640
Dec-984.5994.6484.7144.7554.6884.656
Jan-994.6244.5764.6514.6994.6264.587
Feb-995.2534.6074.6694.6904.6404.616
Mar-995.2315.2605.3345.3305.2705.257
Apr-995.3615.1905.3445.3825.2775.210
May-995.5125.3495.3815.4195.3545.355
Jun-995.7115.4935.6505.6905.5985.502
Jul-995.8315.7035.7545.8155.7445.707
Aug-995.8635.8645.9525.9755.9125.848
Sep-995.7925.8775.9806.0195.9405.969
Oct-995.9525.7535.8665.9325.8545.772
Nov-996.1415.9555.9576.0015.9665.963
Dec-996.3876.1286.1006.1326.1126.134
Jan-006.5576.3956.3956.3796.3746.398
Feb-006.2366.5826.5756.5116.5326.574
Mar-006.0476.2416.4216.3826.3426.359
Apr-006.0396.0446.0385.9966.0276.056
May-006.1166.0546.1186.0606.0716.054
Jun-005.9046.1035.9845.9746.0436.121
Jul-005.9135.8755.9105.9115.9035.904
Aug-005.5735.9196.0075.9515.9435.925
Sep-005.7035.5225.7575.7455.6865.548
Oct-005.6675.6845.7595.7795.7485.694
Nov-005.4105.6865.7805.7395.7245.684
Dec-005.0975.4095.5035.4575.4365.409
Jan-015.1625.0565.1985.2045.1475.077
Feb-014.8595.1225.2225.2495.1735.142
Mar-014.9194.8485.1215.1185.0074.854
Apr-015.3724.9325.1285.1305.0224.925
May-015.4365.3445.4145.5175.4065.358
Jun-015.4775.4255.4735.5775.4755.430
Jul-015.1665.4695.4945.5945.4985.473
Aug-014.8445.1435.2125.3415.2165.155
Sep-014.6824.8624.9955.1264.9804.853
Oct-014.3674.7134.8264.9504.7934.697
Nov-014.9114.3804.4804.6624.4844.373
Dec-015.2064.8714.8545.1314.9584.891
Jan-025.2055.1605.1505.4405.2615.183
Feb-024.9305.1815.0935.3815.2285.193
Mar-025.4604.9204.9485.2205.0474.925
Apr-025.1935.4885.4245.6585.5435.474
May-025.1875.2135.1845.4165.2805.203
Jun-024.9935.1845.0835.3085.1985.186
Jul-024.7164.9764.9255.1615.0224.984
Aug-024.2344.7164.6834.9054.7634.716
Sep-023.7514.2104.2574.4584.2964.222
Oct-024.1003.7043.7373.9153.7733.727
Nov-024.3054.0744.0984.2494.1054.087
Dec-023.9764.2964.3944.5244.3674.301
Jan-034.1373.9764.0144.1304.0063.976
Feb-033.8054.1784.2234.3064.1994.158
Mar-033.9483.8483.9293.9873.8763.826
Apr-034.0133.9434.0584.1434.0193.945
May-033.4833.9954.0744.1814.0754.004
Jun-033.6623.4303.4603.5903.4893.457
Jul-034.5903.6973.6773.7613.6793.680
Aug-034.5924.6334.6844.7784.6564.612
Sep-034.1224.6254.6924.7974.6854.609
Oct-034.4924.1534.1434.2414.1704.137
Nov-034.4584.5474.5194.5954.5304.520
Dec-034.4204.4854.4594.5504.4744.472

Figure 13a. Observed and Predicted Yields, 3-Month Forecast Horizon: 3-Month Yield

Data for Figure 13a immediately follows.

Data for Figure 13a

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-943.0163.1383.1063.491#N/A#N/A
Feb-943.4313.1633.2463.678#N/A#N/A
Mar-943.5363.0543.1703.5993.1143.109
Apr-943.9453.1123.0893.4673.0232.995
May-944.2703.4393.4703.8303.4273.423
Jun-944.2233.8323.7644.0423.7423.752
Jul-944.3534.2764.0994.3384.0914.100
Aug-944.6444.2204.2754.5704.2694.259
Sep-944.7764.2854.2894.5714.2994.294
Oct-945.1384.3514.3854.6654.3624.326
Nov-945.6654.6604.7014.9314.6574.656
Dec-945.6624.9224.9315.1204.9014.887
Jan-955.9325.2045.1175.3035.1465.139
Feb-955.8685.6665.6555.7235.6025.720
Mar-955.8235.6545.5825.6285.5415.667
Apr-955.8095.7575.8435.9165.7115.816
May-955.7425.8305.7655.8465.6505.747
Jun-955.5515.7145.8415.9305.6495.740
Jul-955.5275.6645.8065.9015.5995.704
Aug-955.3985.7395.6705.7475.4855.609
Sep-955.3535.5785.4355.5125.2985.440
Oct-955.4215.5125.4765.5905.2715.386
Nov-955.4245.4985.3935.4765.2235.498
Dec-955.0595.4115.3685.4365.1485.279
Jan-965.0005.3805.2595.3625.0995.238
Feb-964.9825.1685.2845.4295.0425.172
Mar-965.0995.0604.8264.9344.7284.893
Apr-965.1004.9994.8985.0514.7174.844
May-965.1384.9554.9605.1314.7934.836
Jun-965.1445.0975.1395.2574.9235.039
Jul-965.2795.0205.0055.1664.8734.981
Aug-965.2495.2975.1705.2595.0265.157
Sep-965.0575.1775.0585.1834.9725.099
Oct-965.1165.2335.2085.3315.1065.235
Nov-965.0985.1765.2385.3615.0975.219
Dec-965.1204.9245.0665.2144.9155.042
Jan-975.1255.0635.0555.1834.9305.055
Feb-975.1965.1495.0465.1194.9415.082
Mar-975.2865.1975.0585.1424.9925.110
Apr-975.2565.0885.0745.1904.9765.085
May-975.1405.2195.1695.2365.0785.191
Jun-975.1945.3245.3355.3935.2305.339
Jul-975.2035.1605.1955.2855.0865.210
Aug-975.1855.0135.0455.1474.9545.096
Sep-975.0205.2005.1525.2124.9965.133
Oct-975.1735.1365.1405.1914.9775.136
Nov-975.2575.3205.1655.1955.0525.195
Dec-975.3075.1054.9584.9964.8454.999
Jan-985.1585.1245.0115.0614.9025.054
Feb-985.2745.3315.1275.1205.0325.185
Mar-985.1345.3415.1875.1775.0715.222
Apr-984.9465.1495.0515.0704.9475.091
May-984.9975.2915.1685.1445.0305.188
Jun-985.0125.1005.1235.1184.9425.101
Jul-985.0495.0054.8984.8884.8034.966
Aug-984.8465.0544.8644.8414.8244.989
Sep-984.3024.8374.9504.9554.7734.943
Oct-984.3234.7844.8604.8954.7344.905
Nov-984.4904.7004.7204.7494.5754.730
Dec-984.4354.2664.1644.1634.0624.266
Jan-994.4374.2574.1344.2014.0384.257
Feb-994.6424.6074.4724.4344.3444.607
Mar-994.4534.4404.3954.3554.2364.440
Apr-994.5184.4784.3794.3454.2034.478
May-994.6204.6184.5514.5594.4204.618
Jun-994.7344.3584.4464.5074.2754.358
Jul-994.7134.5264.4894.5144.3724.526
Aug-994.9064.4784.5274.5644.4354.478
Sep-994.8074.7824.6784.6804.6234.782
Oct-995.0454.9634.7034.6624.6844.963
Nov-995.2494.9294.8164.8134.7984.929
Dec-995.3274.7114.7074.7454.6514.711
Jan-005.6635.0104.8274.8264.8775.010
Feb-005.7355.1835.1455.1465.1445.183
Mar-005.8275.3805.3485.3355.3215.380
Apr-005.8005.7445.6285.5435.6135.744
May-005.5755.7675.7145.6095.6965.767
Jun-005.8395.7295.8755.7095.7635.729
Jul-006.1945.8075.7275.5275.7275.807
Aug-006.2565.6095.3895.1795.4915.609
Sep-006.1665.7935.8455.6465.7725.793
Oct-006.3086.0826.1505.9896.0266.082
Nov-006.1626.1076.1626.0076.0466.107
Dec-005.8496.1006.0665.9205.9676.100
Jan-014.9666.3646.2296.0776.1466.364
Feb-014.8335.9786.0255.9345.9115.978
Mar-014.2665.5745.6425.6115.5265.574
Apr-013.8534.7294.7904.8704.6814.744
May-013.6054.7324.7924.8544.6434.732
Jun-013.6284.3184.3004.3804.1554.318
Jul-013.5213.8673.8904.0453.8033.864
Aug-013.3353.6263.6103.7793.5093.579
Sep-012.3493.5443.5863.8113.4943.570
Oct-012.0273.4913.5623.8103.3923.462
Nov-011.7823.4663.3903.5953.2433.325
Dec-011.6982.4562.4432.8192.3402.383
Jan-021.7592.2172.1332.4892.0592.102
Feb-021.7571.6711.8702.2691.7081.767
Mar-021.7851.5451.7782.2021.6101.676
Apr-021.7491.6231.8462.2671.6761.758
May-021.7221.7611.8552.2581.6951.776
Jun-021.6891.9121.9792.3121.9001.994
Jul-021.6931.6921.8462.2551.7531.815
Aug-021.6671.5391.7932.2451.7161.757
Sep-021.5431.5651.7282.1881.6491.629
Oct-021.4361.6141.7182.2591.6731.650
Nov-021.2191.4181.6402.1731.5761.541
Dec-021.1871.2771.5082.0141.4321.371
Jan-031.1691.3181.4481.9801.4091.370
Feb-031.2051.1011.3041.7931.2561.183
Mar-031.1041.2591.2661.7311.2711.233
Apr-031.1111.4651.3241.7321.3941.409
May-031.1101.3931.3261.7291.3691.356
Jun-030.8761.0551.2031.6831.2381.177
Jul-030.9401.0951.2131.6781.2721.233
Aug-030.9881.1051.2221.6111.1901.163
Sep-030.9281.2751.0821.4151.1111.165
Oct-030.9371.2721.1641.6101.2041.210
Nov-030.9261.2701.1961.6121.2391.196
Dec-030.9281.2651.1021.5131.1681.132

Figure 13b. Observed and Predicted Yields, 3-Month Forecast Horizon: 2-Year Yield

Data for Figure 13b immediately follows.

Data for Figure 13b

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-944.0793.9263.9484.558#N/A#N/A
Feb-944.6394.1134.1864.822#N/A#N/A
Mar-945.1704.1534.1794.7844.1704.179
Apr-945.6804.1044.0794.6414.0454.033
May-945.9284.5864.6025.1104.5404.535
Jun-946.0875.3175.1795.5625.1275.147
Jul-945.9075.8525.6045.8855.5465.747
Aug-946.0865.8195.7436.0615.6695.891
Sep-946.4976.0605.9026.1675.8336.070
Oct-946.7325.8455.7446.0675.6965.888
Nov-947.2636.0455.9106.2095.8766.067
Dec-947.5036.5426.3556.5486.3326.504
Jan-957.1266.7266.5626.7366.5406.715
Feb-956.6687.1966.9997.0436.9057.201
Mar-956.6727.4237.1267.0586.9877.408
Apr-956.4696.9416.8556.9616.7597.033
May-955.7806.6026.4906.6706.4166.635
Jun-955.7086.5516.4816.7016.4096.621
Jul-955.7926.3176.3156.5826.2446.421
Aug-955.7565.7565.7266.0635.6545.799
Sep-955.7255.7015.6145.9385.5435.722
Oct-955.5335.7535.7256.0825.6465.803
Nov-955.2735.8065.6625.9665.5905.784
Dec-955.0885.7385.6145.9035.5255.740
Jan-964.8705.4855.4445.7645.3445.539
Feb-965.3635.0795.1815.6165.0915.242
Mar-965.6915.0785.0075.3294.9055.110
Apr-965.9404.8644.8795.3234.7934.864
May-966.1615.3545.2555.6645.2195.318
Jun-966.0135.6675.5625.8985.4885.637
Jul-966.1175.8505.7446.0475.6705.902
Aug-966.2316.2445.9836.1985.9246.170
Sep-966.0086.0075.8476.0825.7766.004
Oct-965.6686.0515.9586.1845.8896.092
Nov-965.5086.1316.0576.2895.9846.192
Dec-965.7905.8665.8266.0865.7585.959
Jan-975.8395.6065.5645.8475.4995.683
Feb-976.0085.5275.4145.6655.3575.528
Mar-976.3355.8235.6785.8935.6195.806
Apr-976.1935.7865.6885.9435.6515.822
May-976.1175.9885.8346.0225.7815.990
Jun-975.9916.3106.1616.3066.0926.302
Jul-975.6606.0645.9996.1645.9096.141
Aug-975.8745.9595.9156.0695.8036.060
Sep-975.7125.9415.8276.0065.7405.966
Oct-975.5675.5755.5045.7185.4065.635
Nov-975.7115.9335.7675.9145.6785.896
Dec-975.5785.7345.5805.7105.4745.721
Jan-985.2635.5055.3915.5895.3235.557
Feb-985.4695.7375.5325.6515.4675.710
Mar-985.5035.5735.4415.5795.3535.592
Apr-985.5095.2345.1625.3715.0855.293
May-985.4655.4465.3465.4935.2455.481
Jun-985.4045.4425.3495.5175.2615.492
Jul-985.4185.5205.3555.4465.2655.513
Aug-984.8145.4825.3305.3815.2265.480
Sep-984.2775.2465.2345.3615.1175.372
Oct-984.1675.1965.2405.3615.1145.368
Nov-984.4784.7104.7814.9784.6644.856
Dec-984.5194.2414.2554.3944.1164.309
Jan-994.5314.1114.2344.4804.1034.169
Feb-995.0974.5604.4964.6614.3764.513
Mar-994.9384.5184.4744.6284.3514.504
Apr-995.0114.5604.4344.6134.3424.510
May-995.3545.0634.9525.1034.8665.039
Jun-995.4564.8454.8105.0474.7494.865
Jul-995.5594.9964.9065.0844.8405.019
Aug-995.6505.2315.1785.3185.1115.231
Sep-995.5505.4715.3375.4285.2715.471
Oct-995.7235.7155.4745.5155.4215.715
Nov-995.9315.6385.5755.6245.4915.658
Dec-996.1485.4535.4325.5385.3625.526
Jan-006.5065.6855.6165.6485.5655.715
Feb-006.4415.8625.8005.8485.7655.862
Mar-006.3906.1556.0326.0676.0126.142
Apr-006.5676.5306.3216.2866.3166.453
May-006.5976.4366.2816.2396.2756.420
Jun-006.2806.2976.1766.1026.1636.321
Jul-006.2046.5526.3296.1476.3136.523
Aug-006.0876.5556.3366.0586.2826.540
Sep-005.8856.2216.1686.0446.0966.258
Oct-005.8246.1236.1676.1376.1026.196
Nov-005.5485.9915.9986.0105.9646.104
Dec-005.0515.8615.9355.9545.8515.949
Jan-014.5675.9155.9185.9685.8605.898
Feb-014.3865.4655.5775.7235.5405.563
Mar-014.1864.9115.1285.3695.0875.068
Apr-014.2784.4334.6594.9944.6294.594
May-014.2134.3704.5144.8734.5064.370
Jun-014.2334.2664.3194.6664.3104.266
Jul-013.7744.3014.4134.7524.3644.301
Aug-013.6094.2444.3114.6644.2654.244
Sep-012.8224.1944.3234.7034.2624.194
Oct-012.3703.8063.9514.4403.9213.806
Nov-012.8403.7593.8214.2463.7613.759
Dec-013.0662.9533.1283.6943.0912.953
Jan-023.1532.5902.7123.3122.6972.590
Feb-023.0442.8022.9793.5712.9452.802
Mar-023.6743.0013.1353.7243.0983.001
Apr-023.2163.1013.1973.7563.1513.101
May-023.1873.1003.1033.6513.0553.100
Jun-022.8753.8043.6614.0643.6363.804
Jul-022.2233.2383.2393.7803.2273.238
Aug-022.1093.1173.1433.7183.2013.117
Sep-021.6812.8512.9123.5232.9742.851
Oct-021.6652.2382.5153.2202.5322.238
Nov-022.0391.9952.2962.9952.3531.995
Dec-021.5821.5521.8722.5881.9151.552
Jan-031.6911.6281.9532.6742.0041.628
Feb-031.5101.9852.2402.8822.2911.985
Mar-031.4861.6881.8822.5211.9471.688
Apr-031.4771.9612.0552.6242.1311.961
May-031.3171.7011.8552.4241.9361.701
Jun-031.2991.5041.8052.4421.8921.504
Jul-031.7381.5161.8302.4431.8801.516
Aug-031.9611.3711.5782.1461.6161.371
Sep-031.4621.6431.6592.1491.6871.643
Oct-031.8212.0192.1352.7012.1752.019
Nov-032.0342.1932.2552.7892.3052.193
Dec-031.8391.7641.8242.3611.8861.764

Figure 13c. Observed and Predicted Yields, 3-Month Forecast Horizon: 5-Year Yield

Data for Figure 13c immediately follows.

Data for Figure 13c

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-945.0184.7264.9265.404#N/A#N/A
Feb-945.5875.0385.2375.757#N/A#N/A
Mar-946.2065.1105.2275.7345.1935.196
Apr-946.5924.9685.0745.5505.0465.032
May-946.7235.4825.5816.0115.5345.552
Jun-946.9216.2436.2166.5526.1726.215
Jul-946.6726.6526.5056.7736.4666.535
Aug-946.7546.5916.5866.8686.5426.652
Sep-947.2186.8506.7657.0206.7106.836
Oct-947.4126.5816.5526.8486.5256.624
Nov-947.6736.6846.6576.9396.6206.723
Dec-947.6747.2117.0867.3037.0657.165
Jan-957.4197.3777.2627.4677.2447.347
Feb-956.9617.5947.4527.5377.3897.574
Mar-956.9737.5927.4197.4027.2997.609
Apr-956.7677.2597.2057.3397.1327.347
May-955.9936.8886.8357.0516.8016.941
Jun-955.8946.8636.8447.0846.8036.958
Jul-956.0766.6266.7006.9596.6296.803
Aug-955.9855.9426.0196.3345.9756.096
Sep-955.9125.8515.9496.2315.8805.946
Oct-955.7266.0146.1376.4646.0736.142
Nov-955.4565.9906.0126.2915.9836.025
Dec-955.3075.8855.9246.1815.8425.911
Jan-965.1905.6565.7356.0245.6575.717
Feb-965.6675.2885.4645.8355.4075.474
Mar-966.0435.2595.3085.5735.2365.291
Apr-966.3205.1465.2765.6545.2325.279
May-966.5625.6545.7596.0865.7065.742
Jun-966.3796.0026.0356.3195.9796.024
Jul-966.4936.2386.2676.5266.2106.265
Aug-966.6366.6016.4886.6896.4426.484
Sep-966.3866.3566.3196.5416.2736.322
Oct-966.0076.4246.3946.6176.3556.408
Nov-965.7566.5386.5436.7646.4936.556
Dec-966.1436.2586.2986.5476.2566.325
Jan-976.1825.9365.9756.2495.9616.033
Feb-976.3185.7375.7455.9835.7175.794
Mar-976.6746.1446.0686.2936.0636.122
Apr-976.4926.1246.1116.3616.1066.152
May-976.4126.2806.2076.4186.1906.253
Jun-976.3086.6286.5676.7396.5346.595
Jul-975.8326.3686.3706.5646.3256.396
Aug-976.1306.2616.2836.4756.2166.299
Sep-975.9116.2316.1976.3926.1236.185
Oct-975.6335.7345.7585.9845.7175.806
Nov-975.7596.1346.0756.2505.9966.073
Dec-975.6325.8915.8476.0145.7745.853
Jan-985.3105.5585.6095.8165.5555.645
Feb-985.5125.7485.6765.8265.6325.715
Mar-985.5445.5885.5475.7285.4995.595
Apr-985.5625.2415.3145.5245.2515.322
May-985.4855.4435.4585.6325.3825.469
Jun-985.3855.4565.4985.6795.4195.504
Jul-985.4675.5305.5175.6265.4275.492
Aug-984.8655.4625.4335.5215.3435.411
Sep-984.3475.2415.3045.4645.2205.303
Oct-984.4805.2785.3285.4855.2465.341
Nov-984.5624.7624.8785.0844.8054.882
Dec-984.5914.2794.2874.4564.2144.297
Jan-994.5274.3854.4294.6734.3834.455
Feb-995.2064.5744.6224.7854.5144.584
Mar-995.1694.5494.5964.7364.4894.562
Apr-995.2664.5114.5784.7254.4894.550
May-995.6405.1595.1645.3205.0835.140
Jun-995.7595.0685.1215.3365.0615.120
Jul-995.9225.2225.1925.3735.1435.194
Aug-995.9685.5395.4885.6335.4555.506
Sep-995.8795.7495.6315.7525.6135.653
Oct-996.0456.0035.8105.8885.7935.815
Nov-996.1435.9315.8515.9525.8295.866
Dec-996.3905.7835.7445.8655.7435.777
Jan-006.6606.0045.8735.9485.8575.896
Feb-006.5696.0836.0096.0985.9936.046
Mar-006.2536.3806.2596.3346.2566.299
Apr-006.4566.6686.4726.4946.4776.518
May-006.4536.5556.3766.3916.3966.462
Jun-006.1586.1946.0926.0866.0986.172
Jul-006.1346.4646.2326.1486.2336.283
Aug-005.9326.4166.2366.0706.1796.244
Sep-005.7976.1126.0546.0126.0356.088
Oct-005.7066.0826.0116.0656.0396.092
Nov-005.3895.8645.8295.8845.8515.916
Dec-004.9895.7785.8325.8895.8065.864
Jan-014.8475.7805.7765.8645.7725.824
Feb-014.6995.3425.4435.5955.4475.510
Mar-014.6204.8995.0755.3095.0895.150
Apr-014.9384.7544.9105.2224.9334.979
May-014.9774.7034.7785.0914.8274.830
Jun-015.0674.6874.7305.0354.7624.753
Jul-014.6714.9455.0305.3285.0155.010
Aug-014.4974.9955.0425.3425.0245.022
Sep-014.0555.0465.0545.3665.0575.065
Oct-013.6754.6964.7355.1034.7634.757
Nov-014.1034.5974.5764.8974.5834.586
Dec-014.4474.1424.1594.5984.2044.166
Jan-024.5193.8233.8564.2743.8723.791
Feb-024.3584.0564.2744.6844.2314.185
Mar-025.0034.3874.5204.9424.4914.475
Apr-024.5844.4714.5244.9134.5014.502
May-024.4144.3784.3984.7694.3774.392
Jun-024.1495.0784.9555.2054.9204.991
Jul-023.6364.5894.5804.9444.5974.584
Aug-023.2844.3604.4654.8504.4754.467
Sep-022.6734.1114.2534.6814.2854.258
Oct-022.8763.6093.8574.3913.9143.855
Nov-023.3193.1713.5004.0183.5533.475
Dec-022.8092.5422.9943.5113.0022.749
Jan-033.0442.8023.1943.7543.2282.965
Feb-032.7263.2503.5114.0233.5583.358
Mar-032.8252.8513.1133.6233.1732.922
Apr-032.8873.1963.3143.7753.3953.184
May-032.3512.8253.0193.4863.1002.855
Jun-032.5012.8133.0663.5893.1732.899
Jul-033.3622.8883.1013.6093.1952.957
Aug-033.5132.3502.6983.1142.6932.463
Sep-032.8802.7052.8573.2322.8572.685
Oct-033.2963.5173.6204.0863.6853.498
Nov-033.3873.6363.6914.1373.7713.590
Dec-033.2643.0533.1823.6073.2573.033

Figure 13d. Observed and Predicted Yields, 3-Month Forecast Horizon: 10-Year Yield

Data for Figure 13d immediately follows.

Notes: The figure shows the observed yields for different maturities, together with the 3-month forecast from selected models. See Figure 12 for further details.

Data for Figure 13d

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-945.8505.5285.5735.883#N/A#N/A
Feb-946.2015.9165.9606.295#N/A#N/A
Mar-946.8735.9225.9446.2745.9125.953
Apr-947.1485.7765.7716.0555.7425.776
May-947.2346.0796.2036.4826.1296.201
Jun-947.4546.8846.8177.0396.7566.796
Jul-947.2817.1836.9977.1616.9797.010
Aug-947.2637.0997.0217.1976.9847.065
Sep-947.6787.3757.2197.3637.1857.269
Oct-947.8557.1807.0467.1797.0007.102
Nov-947.8567.1817.1347.2567.0627.154
Dec-947.7427.6557.5207.6037.4617.545
Jan-957.5607.8087.6877.7447.6247.713
Feb-957.1337.7707.6567.6307.5777.714
Mar-957.1997.6517.4507.3317.3487.549
Apr-957.1047.3957.4247.4027.2987.452
May-956.3297.0427.1607.1757.0087.143
Jun-956.2817.0757.2017.2247.0497.174
Jul-956.5446.9507.0597.1176.9597.064
Aug-956.3186.2496.4036.4946.2866.404
Sep-956.2026.2106.3056.3816.1896.302
Oct-956.0436.4606.5646.6786.4496.555
Nov-955.7186.2946.3766.4536.2746.371
Dec-955.5646.1496.2366.3076.1176.229
Jan-965.6055.9526.0506.1515.9456.067
Feb-966.1085.5375.8355.9825.6945.843
Mar-966.3235.4905.5755.6885.4935.616
Apr-966.6345.5355.7075.8805.6115.729
May-966.7876.0806.1786.3256.1096.194
Jun-966.6746.2686.4066.5286.2856.385
Jul-966.7496.5476.6226.7236.5236.610
Aug-966.9026.8126.8206.8816.7046.777
Sep-966.6786.6406.6456.7156.5556.632
Oct-966.3026.6766.6976.7806.6086.691
Nov-966.0146.8016.8756.9456.7666.846
Dec-966.3876.5496.6386.7306.5396.627
Jan-976.4806.2206.3226.4336.2596.343
Feb-976.4885.9766.0356.1245.9546.051
Mar-976.8276.3736.3936.4546.3046.382
Apr-976.6516.4136.4676.5366.3666.450
May-976.5936.4396.5206.5666.4106.489
Jun-976.4296.7726.8546.8846.7376.806
Jul-975.9626.5226.6476.6896.5226.611
Aug-976.2526.4396.5276.5956.4166.514
Sep-976.0356.3426.4786.5286.3226.424
Oct-975.7705.8546.0076.0845.8866.000
Nov-975.8086.2416.3186.3606.1856.278
Dec-975.6836.0006.0566.0975.9366.035
Jan-985.4915.6845.8505.8805.7055.819
Feb-985.5405.7805.8575.8425.7425.835
Mar-985.5745.6215.7355.7555.5925.711
Apr-985.6025.4035.5305.5825.4395.544
May-985.4615.4555.6255.6655.4825.603
Jun-985.3465.4765.6815.7195.5365.651
Jul-985.4195.5605.6225.6405.5355.627
Aug-985.0475.4285.4935.5035.3965.496
Sep-984.4435.2005.4215.4495.2865.405
Oct-984.6685.2355.4125.4735.3045.424
Nov-984.6644.9335.0415.1194.9535.073
Dec-984.5994.3474.4274.4494.3164.440
Jan-994.6244.5504.6654.7734.5864.699
Feb-995.2534.6484.7774.8364.6794.783
Mar-995.2314.5404.7084.7614.5974.709
Apr-995.3614.5904.7274.7544.6204.718
May-995.5125.2015.3365.3705.2115.303
Jun-995.7115.1285.3745.4535.2365.336
Jul-995.8315.3115.4065.4825.3165.402
Aug-995.8635.4245.6595.7165.5405.625
Sep-995.7925.7035.7805.8445.7115.779
Oct-995.9525.9085.9625.9975.8845.933
Nov-996.1415.8305.9786.0325.8925.961
Dec-996.3875.7065.8915.9495.8085.878
Jan-006.5575.9205.9635.9995.9205.975
Feb-006.2366.0856.1066.1376.0706.128
Mar-006.0476.3756.3876.3796.3336.380
Apr-006.0396.5656.5526.4826.4766.517
May-006.1166.2316.4166.3606.3066.362
Jun-005.9045.9936.0375.9675.9896.045
Jul-005.9136.0556.1075.9836.0206.066
Aug-005.5736.0785.9985.8465.9545.994
Sep-005.7035.8555.9335.8765.8765.937
Oct-005.6675.8565.9965.9615.9215.996
Nov-005.4105.5045.7855.7705.6985.785
Dec-005.0975.6725.7975.8215.7665.841
Jan-015.1625.7215.7905.8005.7625.831
Feb-014.8595.3495.4985.5365.4575.548
Mar-014.9194.9945.2205.3195.1885.282
Apr-015.3725.0535.2395.3935.2035.287
May-015.4364.8445.1405.2825.0725.149
Jun-015.4774.9575.1455.2905.0775.143
Jul-015.1665.3535.4535.6595.4295.487
Aug-014.8445.4325.5015.7175.4875.535
Sep-014.6825.4475.5055.7255.4975.551
Oct-014.3675.1785.2565.5345.2775.332
Nov-014.9114.9235.0415.3105.0425.099
Dec-015.2064.7514.8415.1804.8614.902
Jan-025.2054.4984.5584.9224.6074.608
Feb-024.9304.8674.9415.3395.0025.039
Mar-025.4605.1585.2105.6345.2825.318
Apr-025.1935.1715.1435.5595.2385.275
May-025.1874.9585.0055.4055.0795.111
Jun-024.9935.5425.4595.7665.5415.549
Jul-024.7165.2195.2105.5865.3085.322
Aug-024.2345.1645.1165.4785.2285.241
Sep-023.7514.9754.9745.3695.0815.100
Oct-024.1004.6994.7205.1914.8624.889
Nov-024.3054.1434.2964.7224.3844.428
Dec-023.9763.6383.8084.1903.8683.886
Jan-034.1374.0274.1474.5434.2014.212
Feb-033.8054.2404.4154.7634.4244.427
Mar-033.9484.0014.0714.4074.1184.115
Apr-034.0134.2554.2664.5744.3234.310
May-033.4833.8773.9674.2583.9993.991
Jun-033.6623.9274.1004.4214.1314.085
Jul-034.5903.9974.1334.4564.1874.147
Aug-034.5923.4563.5673.8453.6053.586
Sep-034.1223.8143.7564.0133.7993.773
Oct-034.4924.7014.7155.0444.7574.714
Nov-034.4584.6844.7285.0394.7714.733
Dec-034.4204.2554.2044.5054.3004.267

Figure 14a. Observed and Predicted Yields, 6-Month Forecast Horizon: 3-Month Yield

Data for Figure 14a immediately follows.

Data for Figure 14a

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-943.0163.2233.2413.975#N/A#N/A
Feb-943.4313.0803.1813.893#N/A#N/A
Mar-943.5363.0413.1063.783#N/A#N/A
Apr-943.9453.1523.1883.844#N/A#N/A
May-944.2703.1233.3364.064#N/A#N/A
Jun-944.2233.0353.2623.9893.1053.037
Jul-944.3533.1243.1743.8383.0302.948
Aug-944.6443.4673.5464.1803.4213.363
Sep-944.7763.9723.7884.4103.8203.974
Oct-945.1384.3454.1114.6464.1444.258
Nov-945.6654.2174.3414.8354.2564.253
Dec-945.6624.2974.3374.8494.3124.310
Jan-955.9324.3294.4454.9164.3494.307
Feb-955.8684.6614.7475.1544.6404.645
Mar-955.8234.9454.9535.3384.9074.901
Apr-955.8095.1805.1475.5025.1375.118
May-955.7425.6485.6755.8035.5155.568
Jun-955.5515.6065.6015.6375.4065.422
Jul-955.5275.6425.8715.9485.5235.730
Aug-955.3985.7115.7775.8925.4745.654
Sep-955.3535.5745.8575.9765.4495.639
Oct-955.4215.5715.8175.9495.3845.582
Nov-955.4245.6525.6615.7665.2505.453
Dec-955.0595.5325.4255.5435.0755.285
Jan-965.0005.3945.4625.6605.0415.236
Feb-964.9825.4325.3795.5205.0175.220
Mar-965.0995.3415.3565.4574.9215.151
Apr-965.1005.2615.2595.3794.8495.083
May-965.1384.9655.3105.4324.7384.808
Jun-965.1445.0334.8334.9494.4914.667
Jul-965.2794.8724.8905.1164.4704.588
Aug-965.2494.8814.9785.2294.6204.715
Sep-965.0574.9825.1255.3454.7184.814
Oct-965.1164.8755.0235.2754.6924.753
Nov-965.0985.2325.1595.3674.9014.988
Dec-965.1205.0565.0665.2794.8354.898
Jan-975.1255.1285.2305.4114.9725.128
Feb-975.1965.0775.2595.4574.9685.077
Mar-975.2864.8145.0975.3104.7764.814
Apr-975.2564.9895.0785.2594.7924.989
May-975.1405.1355.0535.1594.8035.135
Jun-975.1945.1135.0595.2144.8745.113
Jul-975.2035.0055.1025.2694.8645.005
Aug-975.1855.1485.1815.3014.9685.148
Sep-975.0205.2985.3465.4655.1405.286
Oct-975.1735.0495.2075.3454.9405.107
Nov-975.2574.9425.0745.2124.8084.942
Dec-975.3075.1555.1515.2704.8485.041
Jan-985.1585.0415.1455.1994.7795.041
Feb-985.2745.3035.1565.2314.9165.124
Mar-985.1345.0404.9515.0204.6905.040
Apr-984.9465.0095.0275.0504.7205.009
May-984.9975.2595.1345.0794.8745.259
Jun-985.0125.2615.1915.1274.8985.261
Jul-985.0495.1525.0715.0284.7955.152
Aug-984.8465.2465.1575.0914.8455.246
Sep-984.3025.0535.1385.0754.7705.053
Oct-984.3235.0314.9064.8514.6735.031
Nov-984.4905.0304.8644.7824.6785.030
Dec-984.4354.6714.9754.8814.5614.671
Jan-994.4374.6494.9114.8304.5324.833
Feb-994.6424.6044.7494.6854.3834.604
Mar-994.4534.1614.1884.0693.8594.103
Apr-994.5184.2274.1744.1863.8764.095
May-994.6204.6454.4684.3804.1974.380
Jun-994.7344.4304.4034.2894.0634.240
Jul-994.7134.4634.3884.2804.0404.200
Aug-994.9064.4894.5644.5454.2604.377
Sep-994.8074.2944.4874.5334.1514.294
Oct-995.0454.4854.5064.5384.2644.485
Nov-995.2494.3784.5664.5934.3244.378
Dec-995.3274.7844.6994.7124.5634.784
Jan-005.6635.0474.6974.7164.6775.047
Feb-005.7354.8714.8254.8424.7364.871
Mar-005.8274.6994.7574.7754.6064.699
Apr-005.8004.9664.8524.8394.8294.966
May-005.5755.1235.1765.1315.0795.147
Jun-005.8395.3525.3625.3235.2745.356
Jul-006.1945.6955.6355.4955.5645.695
Aug-006.2565.7595.7325.5365.6545.759
Sep-006.1665.6485.8955.5585.6635.648
Oct-006.3085.7655.7515.3785.6695.765
Nov-006.1625.6205.3995.0315.4365.620
Dec-005.8495.8005.8595.4885.6815.800
Jan-014.9665.9116.1465.8195.8635.911
Feb-014.8336.0646.1965.8175.9076.064
Mar-014.2666.0606.0465.7625.8116.060
Apr-013.8536.2916.2055.9065.9956.291
May-013.6055.8026.0305.7605.7095.802
Jun-013.6285.4035.6725.4785.3315.403
Jul-013.5214.6084.8264.8774.5414.608
Aug-013.3354.6664.8144.8604.5214.666
Sep-012.3494.3154.3054.4614.0854.210
Oct-012.0273.9293.9044.2273.7653.898
Nov-011.7823.6673.6224.0103.4793.621
Dec-011.6983.4793.6104.0323.4253.539
Jan-021.7593.5553.5954.0423.3483.464
Feb-021.7573.5303.3853.8223.2003.336
Mar-021.7852.5132.4963.1812.3702.396
Apr-021.7492.5132.2052.8842.1752.247
May-021.7221.7801.9462.7201.7631.792
Jun-021.6891.6101.8832.6871.6731.682
Jul-021.6931.6481.9392.7221.7111.739
Aug-021.6671.8561.9442.6961.7661.815
Sep-021.5432.0422.0552.7372.0252.122
Oct-021.4361.7541.9592.7011.8791.931
Nov-021.2191.5571.9282.6761.8391.837
Dec-021.1871.6591.8682.6351.8031.776
Jan-031.1691.6841.8442.7241.8091.783
Feb-031.2051.4111.7962.5741.6651.622
Mar-031.1041.2891.6712.3711.4981.470
Apr-031.1111.3591.5882.4081.5141.468
May-031.1101.1351.4572.2371.3981.340
Jun-030.8761.4341.4062.1641.4581.445
Jul-030.9401.7641.4402.1801.6521.605
Aug-030.9881.6021.4402.1371.5771.525
Sep-030.9281.2101.3632.1261.4391.414
Oct-030.9371.2771.3562.1251.4631.447
Nov-030.9261.3761.3571.9691.3321.346
Dec-030.9281.6521.1661.8231.3301.424

Figure 14b. Observed and Predicted Yields, 6-Month Forecast Horizon: 2-Year Yield

Data for Figure 14b immediately follows.

Data for Figure 14b

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-944.0794.0814.2285.226#N/A#N/A
Feb-944.6393.7513.9735.007#N/A#N/A
Mar-945.1703.8093.9594.921#N/A#N/A
Apr-945.6803.8854.0314.962#N/A#N/A
May-945.9284.0344.2645.261#N/A#N/A
Jun-946.0874.0844.2575.2164.1494.084
Jul-945.9074.0624.1535.0434.0314.062
Aug-946.0864.5524.6665.4474.5014.552
Sep-946.4975.3625.2015.8585.1275.362
Oct-946.7325.8385.6116.0735.5115.838
Nov-947.2635.7485.7896.1985.5765.671
Dec-947.5035.9945.9306.2955.7455.926
Jan-957.1265.7675.7826.2185.6095.774
Feb-956.6685.9925.9406.3615.8005.967
Mar-956.6726.4986.3636.6466.2486.419
Apr-956.4696.6546.5736.8056.4426.609
May-955.7807.1237.0066.9536.7387.192
Jun-955.7087.3237.1286.8096.7527.387
Jul-955.7926.8106.8676.8916.5497.011
Aug-955.7566.4816.4906.7016.2586.621
Sep-955.7256.4156.4846.7546.2446.603
Oct-955.5336.2206.3216.6706.0886.417
Nov-955.2735.6895.7256.2265.5375.811
Dec-955.0885.6645.6166.0775.4155.642
Jan-964.8705.6575.7186.2665.5145.780
Feb-965.3635.7485.6596.1045.4615.639
Mar-965.6915.6765.6136.0105.3805.512
Apr-965.9405.3915.4535.8845.1915.439
May-966.1614.9305.2135.7904.9255.082
Jun-966.0135.0625.0335.4424.7654.912
Jul-966.1174.7784.8905.5644.6744.808
Aug-966.2315.3095.2815.8695.1305.244
Sep-966.0085.5685.5586.0515.3485.424
Oct-965.6685.7185.7596.1475.5165.599
Nov-965.5086.1625.9776.2795.8005.924
Dec-965.7905.8885.8536.1555.6455.818
Jan-975.8395.9415.9766.2505.7595.956
Feb-976.0086.0186.0736.3565.8476.097
Mar-976.3355.7455.8516.1705.6215.854
Apr-976.1935.5325.5885.9725.3965.586
May-976.1175.5065.4315.7695.2645.524
Jun-975.9915.7385.6815.9795.5145.718
Jul-975.6605.6995.7126.0415.5505.723
Aug-975.8745.9025.8446.0855.6695.853
Sep-975.7126.2466.1706.3395.9746.209
Oct-975.5675.9366.0076.1875.7505.998
Nov-975.7115.8565.9386.0835.6406.054
Dec-975.5785.8685.8306.0575.5975.911
Jan-985.2635.4795.5165.7815.2535.638
Feb-985.4695.8865.7665.9535.5495.908
Mar-985.5035.6525.5795.7285.3285.724
Apr-985.5095.3965.4115.6185.1775.545
May-985.4655.6575.5455.6305.3265.715
Jun-985.4045.4895.4535.5895.2185.585
Jul-985.4185.2245.1955.4304.9875.305
Aug-984.8145.3895.3525.5175.1085.482
Sep-984.2775.3815.3745.5395.1275.500
Oct-984.1675.5125.3755.4185.1385.539
Nov-984.4785.4425.3435.3245.0865.492
Dec-984.5195.0965.2635.3274.9425.348
Jan-994.5315.0745.2925.3204.9425.355
Feb-995.0974.6454.8235.0244.5444.845
Mar-994.9384.1544.2984.3933.9724.333
Apr-995.0114.0904.2914.5874.0054.231
May-995.3544.5914.5204.7244.2904.530
Jun-995.4564.5134.5074.6544.2374.498
Jul-995.5594.5494.4684.6434.2354.447
Aug-995.6504.9464.9745.1134.7264.922
Sep-995.5504.7734.8575.1264.6474.810
Oct-995.7234.9464.9345.1494.7494.942
Nov-995.9315.1335.2165.3254.9915.232
Dec-996.1485.4505.3635.4435.1965.424
Jan-006.5065.7515.4785.5295.3765.601
Feb-006.4415.5635.5865.6135.4025.599
Mar-006.3905.4165.4795.5355.2885.551
Apr-006.5675.6345.6395.6065.4805.730
May-006.5975.7945.8275.8085.6805.915
Jun-006.2806.0996.0456.0255.9376.151
Jul-006.2046.4526.3246.1826.2216.479
Aug-006.0876.4016.2966.1356.1976.429
Sep-005.8856.2176.1915.9526.0536.330
Oct-005.8246.4946.3455.9186.1966.523
Nov-005.5486.5096.3415.7386.1226.540
Dec-005.0516.2166.1825.8815.9996.277
Jan-014.5676.0016.1626.0445.9846.179
Feb-014.3865.9836.0305.9345.8876.088
Mar-014.1865.8735.9275.9205.7785.940
Apr-014.2785.9115.9065.9615.8115.917
May-014.2135.3895.5885.7415.4645.570
Jun-014.2334.8505.1635.4645.0335.090
Jul-013.7744.3944.6985.1944.5994.628
Aug-013.6094.3904.5475.1064.5144.439
Sep-012.8224.3184.3384.9244.3274.281
Oct-012.3704.3784.4365.0204.3754.423
Nov-012.8404.3054.3304.9494.2684.283
Dec-013.0664.1764.3494.9694.2374.251
Jan-023.1533.9214.0014.8153.9773.959
Feb-023.0443.8703.8434.6023.8153.870
Mar-023.6743.0483.1924.1843.2023.048
Apr-023.2162.9062.8143.8702.9162.700
May-023.1872.9413.0684.0623.0402.948
Jun-022.8753.0913.2364.2063.1793.129
Jul-022.2233.1603.2894.1983.2043.199
Aug-022.1093.2143.1994.0973.1463.153
Sep-021.6813.9183.7334.3763.6983.778
Oct-021.6653.3203.3454.2053.3413.294
Nov-022.0393.1633.2654.1363.3133.163
Dec-021.5822.9573.0444.0163.1362.957
Jan-031.6912.3342.6463.8622.7502.334
Feb-031.5102.0352.4533.5702.5252.035
Mar-031.4861.6102.0483.1672.0971.774
Apr-031.4771.6922.1023.3232.2031.815
May-031.3172.0282.3813.4352.4552.145
Jun-031.2991.8602.0303.1442.2011.822
Jul-031.7382.2272.1813.2392.4252.033
Aug-031.9611.9011.9833.0312.2031.796
Sep-031.4621.6651.9633.0812.1541.700
Oct-031.8211.6941.9743.0832.1431.710
Nov-032.0341.6191.7302.7121.8391.553
Dec-031.8391.9641.7662.7301.9531.678

Figure 14c. Observed and Predicted Yields, 6-Month Forecast Horizon: 5-Year Yield

Data for Figure 14c immediately follows.

Data for Figure 14c

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-945.0184.9945.3026.079#N/A#N/A
Feb-945.5874.5714.9885.792#N/A#N/A
Mar-946.2064.5894.9495.699#N/A#N/A
Apr-946.5924.6174.9945.722#N/A#N/A
May-946.7234.9145.3006.094#N/A#N/A
Jun-946.9214.9935.2906.0635.1404.993
Jul-946.6724.8705.1355.8594.9974.870
Aug-946.7545.3935.6316.2655.4675.393
Sep-947.2186.2166.2256.7596.1246.216
Oct-947.4126.5876.5056.8986.3926.495
Nov-947.6736.4896.6196.9586.4366.538
Dec-947.6746.7556.7837.0966.5986.713
Jan-957.4196.4806.5836.9536.4216.598
Feb-956.9616.6086.6837.0506.5336.704
Mar-956.9737.1467.0947.3646.9667.074
Apr-956.7677.3017.2777.5057.1387.281
May-955.9937.5197.4657.4647.2447.483
Jun-955.8947.5067.4327.2117.1077.413
Jul-956.0767.1487.2307.2976.9747.261
Aug-955.9856.7866.8547.0976.6846.933
Sep-955.9126.7536.8687.1486.6846.944
Oct-955.7266.5406.7267.0546.5226.780
Nov-955.4565.8756.0456.5085.9146.190
Dec-955.3075.8045.9746.3825.8106.061
Jan-965.1905.9276.1556.6435.9946.241
Feb-965.6675.9296.0306.4375.9086.131
Mar-966.0435.8195.9456.3055.7586.004
Apr-966.3205.5635.7666.1625.5695.836
May-966.5625.1575.5196.0245.3195.626
Jun-966.3795.2175.3525.7085.1605.404
Jul-966.4935.0565.3115.8895.1765.417
Aug-966.6365.6135.7976.2795.6685.831
Sep-966.3865.9116.0486.4665.8926.030
Oct-966.0076.1286.2926.6206.1036.245
Nov-965.7566.5236.4906.7656.3486.463
Dec-966.1436.2536.3356.6146.1766.341
Jan-976.1826.3246.4176.6866.2586.428
Feb-976.3186.4326.5646.8296.3856.552
Mar-976.6746.1496.3296.6296.1516.333
Apr-976.4925.8596.0076.3735.8926.082
May-976.4125.6965.7716.1005.6625.858
Jun-976.3086.0636.0836.3845.9886.152
Jul-975.8326.0436.1426.4606.0336.199
Aug-976.1306.1986.2276.4906.1046.267
Sep-975.9116.5606.5836.7796.4376.576
Oct-975.6336.2526.3906.6006.2006.375
Nov-975.7596.1586.3136.5036.0866.273
Dec-975.6326.1486.2116.4546.0106.202
Jan-985.3105.6385.7846.0715.6145.824
Feb-985.5126.0686.0826.3085.8966.086
Mar-985.5445.8025.8606.0585.6655.862
Apr-985.5625.4535.6415.8785.4555.676
May-985.4855.6645.7005.8515.5345.728
Jun-985.3855.4965.5735.7835.4085.624
Jul-985.4675.1955.3535.6205.1925.420
Aug-984.8655.3615.4755.6995.2885.482
Sep-984.3475.3755.5295.7425.3255.512
Oct-984.4805.4895.5415.6445.3335.494
Nov-984.5625.4015.4545.5185.2455.408
Dec-984.5915.1055.3475.4845.0985.297
Jan-994.5275.1645.3875.4975.1275.312
Feb-995.2064.6904.9355.1734.7384.919
Mar-995.1694.1794.3554.5074.1194.310
Apr-995.2664.3254.4984.8044.3234.512
May-995.6404.5574.6604.8854.4644.629
Jun-995.7594.5104.6424.8064.4214.568
Jul-995.9224.4684.6224.7984.4274.545
Aug-995.9685.0505.1955.3644.9825.093
Sep-995.8794.9825.1685.4314.9865.114
Oct-996.0455.1535.2235.4565.0755.192
Nov-996.1435.4515.5305.6625.3665.480
Dec-996.3905.7095.6555.7885.5545.647
Jan-006.6605.9995.8135.9175.7495.809
Feb-006.5695.8495.8655.9645.7555.832
Mar-006.2535.7305.7845.8855.6815.752
Apr-006.4565.9515.8995.9375.7895.875
May-006.4536.0216.0386.0945.9286.024
Jun-006.1586.3246.2746.3246.1966.275
Jul-006.1346.6026.4816.4376.3996.496
Aug-005.9326.5216.3966.3416.3386.439
Sep-005.7976.1476.1226.0156.0336.161
Oct-005.7066.4406.2626.0076.1536.271
Nov-005.3896.3866.2555.8506.0536.177
Dec-004.9896.1166.0835.9315.9836.117
Jan-014.8476.0056.0336.0485.9776.153
Feb-014.6995.8705.8775.8865.8325.992
Mar-014.6205.7985.8485.9205.7935.949
Apr-014.9385.7915.7875.9225.7805.933
May-014.9775.3055.4835.6775.4445.602
Jun-015.0674.8705.1365.4505.1065.312
Jul-014.6714.7364.9755.4234.9515.102
Aug-014.4974.7354.8395.3224.8844.997
Sep-014.0554.7374.7755.2714.8114.920
Oct-013.6754.9995.0685.5505.0375.140
Nov-014.1035.0395.0755.5665.0345.128
Dec-014.4475.0385.0955.5765.0505.139
Jan-024.5194.7794.7865.4084.8324.914
Feb-024.3584.6684.6025.1874.6464.726
Mar-025.0034.1944.2144.9774.2984.367
Apr-024.5844.0313.9274.7064.0564.094
May-024.4144.1314.3315.0424.3014.300
Jun-024.1494.4244.5795.2834.5364.541
Jul-023.6364.4834.5765.2264.5294.541
Aug-023.2844.4194.4455.0914.4344.438
Sep-022.6735.1154.9775.4104.9364.935
Oct-022.8764.6084.6315.2434.6674.698
Nov-023.3194.3584.5315.1484.5434.541
Dec-022.8094.1404.3245.0414.3914.381
Jan-033.0443.6193.9294.8794.0694.040
Feb-032.7263.1533.6074.4643.6883.669
Mar-032.8252.5343.1253.9713.1523.172
Apr-032.8872.7933.2994.2593.3793.354
May-032.3513.2423.6154.4403.6703.648
Jun-032.5012.9323.2204.1053.3603.244
Jul-033.3623.3373.3964.2453.6053.478
Aug-033.5132.9273.1143.9593.3023.175
Sep-032.8802.9013.1904.0823.3713.260
Oct-033.2962.9853.2124.1023.3893.261
Nov-033.3872.4902.8163.5632.8732.762
Dec-033.2642.8862.9283.6833.0522.935

Figure 14d. Observed and Predicted Yields, 6-Month Forecast Horizon: 10-Year Yield

Data for Figure 14d immediately follows.

Notes: The figure shows the observed yields for different maturities, together with the 6-month forecast from selected models. See Figure 12 for further details.

Data for Figure 14d

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-945.8505.8205.9746.514#N/A#N/A
Feb-946.2015.3765.6536.203#N/A#N/A
Mar-946.8735.3845.5986.098#N/A#N/A
Apr-947.1485.3985.6316.109#N/A#N/A
May-947.2345.7766.0046.526#N/A#N/A
Jun-947.4545.7875.9906.5005.8435.843
Jul-947.2815.6585.8196.2735.6795.672
Aug-947.2635.9716.2446.6646.0526.056
Sep-947.6786.8406.8347.1856.6926.849
Oct-947.8557.1067.0087.2616.8977.058
Nov-947.8566.9877.0517.2786.8847.078
Dec-947.7427.2687.2387.4337.0777.327
Jan-957.5607.0647.0687.2686.9047.024
Feb-957.1337.0907.1527.3486.9827.102
Mar-957.1997.5777.5267.6617.3707.458
Apr-957.1047.7197.6917.7877.5297.644
May-956.3297.6857.6657.6187.4677.635
Jun-956.2817.5567.4587.2617.2187.490
Jul-956.5447.2747.4357.4137.1847.513
Aug-956.3186.9247.1637.2386.9227.182
Sep-956.2026.9517.2057.2966.9617.233
Oct-956.0436.8507.0687.2076.8827.091
Nov-955.7186.1616.4166.6386.2496.483
Dec-955.5646.1426.3236.5146.1536.374
Jan-965.6056.3606.5716.8216.3956.606
Feb-966.1086.2186.3876.5816.2276.427
Mar-966.3236.0686.2536.4256.0676.285
Apr-966.6345.8456.0736.2785.8946.127
May-966.7875.3925.8696.1395.6435.917
Jun-966.6745.4295.6185.8165.4595.690
Jul-966.7495.4305.7346.0625.5815.809
Aug-966.9026.0296.2006.4776.0916.256
Sep-966.6786.1756.4176.6526.2286.411
Oct-966.3026.4366.6346.8156.4466.607
Nov-966.0146.7346.8216.9596.6376.774
Dec-966.3876.5356.6526.7956.4866.635
Jan-976.4806.5736.7116.8566.5406.697
Feb-976.4886.6936.8877.0166.6876.838
Mar-976.8276.4346.6576.8146.4616.628
Apr-976.6516.1336.3446.5456.2116.380
May-976.5935.9216.0636.2365.9266.111
Jun-976.4296.2846.4036.5466.2526.409
Jul-975.9626.3226.4856.6326.3146.474
Aug-976.2526.3496.5336.6466.3506.505
Sep-976.0356.7006.8666.9426.6676.801
Oct-975.7706.4036.6606.7486.4306.599
Nov-975.8086.3316.5496.6496.3216.501
Dec-975.6836.2556.4946.6036.2396.426
Jan-985.4915.7506.0336.1795.8206.035
Feb-985.5406.1686.3336.4356.1186.296
Mar-985.5745.9056.0746.1665.8636.052
Apr-985.6025.5705.8795.9625.6435.856
May-985.4615.6865.8835.9045.6795.869
Jun-985.3465.5165.7655.8345.5355.754
Jul-985.4195.3415.5785.6845.4105.613
Aug-985.0475.3625.6615.7505.4255.648
Sep-984.4435.3875.7215.8015.4775.689
Oct-984.6685.5115.6655.6975.4855.661
Nov-984.6645.3615.5335.5495.3445.531
Dec-984.5995.0595.4635.5075.2055.429
Jan-994.6245.1165.4645.5265.2275.445
Feb-995.2534.8455.0975.2164.9175.136
Mar-995.2314.2234.4974.5244.2544.490
Apr-995.3614.4694.7364.8934.5534.765
May-995.5124.6134.8374.9394.6624.856
Jun-995.7114.4884.7734.8464.5654.765
Jul-995.8314.5344.7894.8404.5914.774
Aug-995.8635.0895.3705.4395.1445.315
Sep-995.7925.0385.4205.5485.1825.358
Oct-995.9525.2385.4445.5705.2715.428
Nov-996.1415.3425.6945.7725.4825.631
Dec-996.3875.6655.8115.9035.6765.800
Jan-006.5575.9075.9856.0495.8595.952
Feb-006.2365.7545.9996.0755.8435.968
Mar-006.0475.6565.9295.9975.7685.891
Apr-006.0395.8715.9886.0305.8835.989
May-006.1166.0226.1306.1706.0326.145
Jun-005.9046.3196.4006.4076.2936.390
Jul-005.9136.5016.5586.4836.4256.514
Aug-005.5736.2056.4326.3676.2796.381
Sep-005.7035.9466.0575.9675.9676.081
Oct-005.6676.0366.1225.9435.9916.083
Nov-005.4106.0506.0185.7625.8895.978
Dec-005.0975.8585.9595.8715.8675.981
Jan-015.1625.7756.0035.9915.8986.046
Feb-014.8595.5075.8175.8115.7155.868
Mar-014.9195.6855.8175.8785.7865.926
Apr-015.3725.7215.8015.8735.7965.932
May-015.4365.3015.5195.6235.4815.651
Jun-015.4774.9485.2545.4405.2235.397
Jul-015.1665.0155.2705.5455.2255.380
Aug-014.8444.8575.1695.4515.1305.264
Sep-014.6824.9875.1685.4605.1265.244
Oct-014.3675.3895.4785.8155.4475.549
Nov-014.9115.4635.5215.8735.4945.564
Dec-015.2065.4345.5215.8735.4905.570
Jan-025.2055.2485.2925.7365.3365.426
Feb-024.9304.9875.0735.5065.1005.172
Mar-025.4604.7934.8775.4244.9264.987
Apr-025.1934.6874.6295.1974.7584.778
May-025.1874.9385.0015.5685.0535.096
Jun-024.9935.1975.2625.8495.3045.347
Jul-024.7165.1925.1945.7595.2535.299
Aug-024.2345.0045.0645.6125.1125.150
Sep-023.7515.5915.5065.9045.5545.555
Oct-024.1005.2485.2655.7785.3475.359
Nov-024.3055.1695.1765.6705.2695.282
Dec-023.9765.0025.0425.5985.1485.166
Jan-034.1374.7004.7855.4924.9544.994
Feb-033.8054.1174.3765.0054.4734.499
Mar-033.9483.6173.9074.4843.9664.031
Apr-034.0133.9974.2234.8594.2884.314
May-033.4834.2144.4785.0274.4814.497
Jun-033.6624.0494.1494.7104.2334.228
Jul-034.5904.3594.3374.8704.4584.436
Aug-034.5923.9454.0414.5574.1324.127
Sep-034.1223.9824.1744.7304.2534.237
Oct-034.4924.0584.2044.7644.3014.295
Nov-034.4583.5583.6684.1323.7333.734
Dec-034.4203.9543.8354.3003.9333.879

Figure 15a. Observed and Predicted Yields, 12-Month Forecast Horizon: 3-Month Yield

Data for Figure 15a immediately follows.

Data for Figure 15a

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-943.0163.8963.4905.005#N/A#N/A
Feb-943.4313.2063.3814.888#N/A#N/A
Mar-943.5362.7403.3724.871#N/A#N/A
Apr-943.9452.5853.3364.906#N/A#N/A
May-944.2702.9503.4734.872#N/A#N/A
Jun-944.2233.1703.3924.641#N/A#N/A
Jul-944.3533.3323.3974.591#N/A#N/A
Aug-944.6443.1413.3394.461#N/A#N/A
Sep-944.7763.1083.2724.344#N/A#N/A
Oct-945.1383.2073.3464.382#N/A#N/A
Nov-945.6653.1433.4814.645#N/A#N/A
Dec-945.6623.0713.4094.5793.0382.912
Jan-955.9323.2053.3284.4082.9902.855
Feb-955.8683.5183.6654.7263.3463.240
Mar-955.8234.1353.9014.9903.9013.927
Apr-955.8094.4934.2215.1514.1944.203
May-955.7424.2574.4225.2794.1824.110
Jun-955.5514.3594.4215.3154.2774.217
Jul-955.5274.3454.5185.3354.2524.152
Aug-955.3984.6694.8025.5234.5304.428
Sep-955.3534.9725.0025.7064.8334.833
Oct-955.4215.1465.1865.8435.0245.024
Nov-955.4245.5625.6915.9885.2715.364
Dec-955.0595.4725.6165.7505.0785.319
Jan-965.0005.3805.8706.0515.0955.337
Feb-964.9825.4345.7805.9965.0605.286
Mar-965.0995.2415.8506.0744.9835.305
Apr-965.1005.2455.8036.0434.8975.150
May-965.1385.3475.6585.8004.7605.015
Jun-965.1445.2715.4285.6044.6164.872
Jul-965.2795.0705.4695.7714.5804.838
Aug-965.2495.1875.3965.6034.6124.945
Sep-965.0575.1035.3735.5134.5014.862
Oct-965.1164.9805.2815.4234.3954.776
Nov-965.0984.5825.3255.4404.1904.664
Dec-965.1204.8274.8634.9954.0674.481
Jan-975.1254.6054.9275.2104.0444.453
Feb-975.1964.6885.0085.3844.3254.671
Mar-975.2864.7525.1595.4964.3764.744
Apr-975.2564.6305.0605.4704.3784.740
May-975.1405.0915.2015.5644.6904.985
Jun-975.1944.8965.1125.4604.5964.905
Jul-975.2034.9735.2675.5664.7255.031
Aug-975.1854.9195.2905.6354.7195.028
Sep-975.0204.6435.1295.4874.5004.795
Oct-975.1734.8405.1105.3964.5224.840
Nov-975.2575.0345.0865.2434.5464.825
Dec-975.3074.9895.1015.3544.6524.909
Jan-985.1584.8775.1365.4164.6454.841
Feb-985.2745.0255.2145.4334.7465.027
Mar-985.1345.1975.3695.6114.9425.204
Apr-984.9464.8495.2315.4774.6434.962
May-984.9974.7395.0935.3574.4964.735
Jun-985.0124.9685.1715.3954.5504.777
Jul-985.0494.8045.1685.2434.4104.777
Aug-984.8465.1525.1855.3234.6574.957
Sep-984.3024.8784.9895.1004.4134.744
Oct-984.3234.7995.0635.0714.3954.723
Nov-984.4905.0965.1695.0644.5884.946
Dec-984.4355.0825.2225.0874.5824.905
Jan-994.4375.0435.0984.9894.5154.937
Feb-994.6425.0775.1885.0424.5184.846
Mar-994.4534.8945.1675.0434.4624.908
Apr-994.5184.9674.9434.8424.4444.863
May-994.6204.9424.9104.7454.4374.865
Jun-994.7344.4355.0154.8104.1984.687
Jul-994.7134.4094.9414.7764.1654.659
Aug-994.9064.4164.7864.6104.0454.517
Sep-994.8073.9764.2483.9573.4974.010
Oct-995.0454.0834.2234.1793.5774.034
Nov-995.2494.5744.5164.3193.9534.380
Dec-995.3274.3324.4554.2163.7974.255
Jan-005.6634.3784.4474.2093.8074.246
Feb-005.7354.3274.6234.5624.0214.348
Mar-005.8274.1834.5394.5993.9514.249
Apr-005.8004.4124.5614.6054.0994.441
May-005.5754.2754.6164.6824.1464.226
Jun-005.8394.7664.7474.8034.4664.625
Jul-006.1945.1334.7504.8424.6834.832
Aug-006.2564.8454.8794.9304.6454.711
Sep-006.1664.7064.8014.8654.5314.636
Oct-006.3084.9534.8964.9084.7474.838
Nov-006.1625.0755.2095.1514.9615.137
Dec-005.8495.3295.3925.3465.1805.358
Jan-014.9665.6495.6605.4735.4585.654
Feb-014.8335.7425.7475.4735.5505.745
Mar-014.2665.5625.9045.3795.4625.721
Apr-013.8535.7195.7605.2235.5165.738
May-013.6055.5875.4094.9025.2715.504
Jun-013.6285.7255.8525.3025.4735.784
Jul-013.5215.6706.1455.5905.5425.891
Aug-013.3355.8716.1755.5525.6116.013
Sep-012.3495.8676.0325.5405.5185.944
Oct-012.0276.0846.2015.6535.7206.097
Nov-011.7825.5096.0255.4955.3505.750
Dec-011.6985.1125.6675.2634.9705.425
Jan-021.7594.3944.8334.8764.2644.599
Feb-021.7574.5094.8214.8494.2894.681
Mar-021.7854.2484.3314.5723.9484.300
Apr-021.7493.9133.9394.5003.6904.028
May-021.7223.6593.6744.3633.4443.755
Jun-021.6893.3953.6714.3733.3453.693
Jul-021.6933.5833.6524.3733.3523.664
Aug-021.6673.5883.4684.1523.2413.542
Sep-021.5432.6752.6353.7062.5362.792
Oct-021.4362.9612.3593.4532.5462.681
Nov-021.2192.0692.1303.3982.0522.282
Dec-021.1871.8582.0773.4261.9882.226
Jan-031.1691.8702.1353.4192.0012.295
Feb-031.2052.1802.1503.3662.1482.382
Mar-031.1042.4582.2623.4172.4952.661
Apr-031.1112.1652.1773.3882.3652.500
May-031.1101.9422.1463.3422.3042.440
Jun-030.8762.1182.0863.3122.3232.435
Jul-030.9402.1102.0633.3972.2962.397
Aug-030.9881.7532.0083.1582.0462.166
Sep-030.9281.6211.8832.8831.8211.934
Oct-030.9371.6861.7993.0271.8601.963
Nov-030.9261.4741.6672.9041.7631.883
Dec-030.9281.9211.6172.7981.9081.969

Figure 15b. Observed and Predicted Yields, 12-Month Forecast Horizon: 2-Year Yield

Data for Figure 15b immediately follows.

Data for Figure 15b

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-944.0794.7134.7406.448#N/A#N/A
Feb-944.6393.8724.4486.237#N/A#N/A
Mar-945.1703.5934.4156.214#N/A#N/A
Apr-945.6803.3154.2896.240#N/A#N/A
May-945.9283.8704.5116.165#N/A#N/A
Jun-946.0873.8864.3075.837#N/A#N/A
Jul-945.9074.0734.3775.789#N/A#N/A
Aug-946.0863.7054.1365.568#N/A#N/A
Sep-946.4973.7644.1235.457#N/A#N/A
Oct-946.7323.8314.1875.477#N/A#N/A
Nov-947.2633.9564.3985.807#N/A#N/A
Dec-947.5034.0144.3885.7614.0674.014
Jan-957.1264.0324.2915.5643.9714.032
Feb-956.6684.4974.7675.9094.4064.497
Mar-956.6725.3785.2856.2915.1105.378
Apr-956.4695.8265.6856.4075.4515.498
May-955.7805.6595.8436.4785.4325.498
Jun-955.7085.9135.9786.5715.6075.670
Jul-955.7925.6795.8266.4995.4525.479
Aug-955.7565.9145.9746.6265.6555.685
Sep-955.7256.4226.3846.8666.1006.129
Oct-955.5336.5476.5816.9936.2636.433
Nov-955.2736.9727.0016.9876.4676.645
Dec-955.0887.1267.1166.7136.3836.637
Jan-964.8706.5606.8486.9196.1726.559
Feb-965.3636.2486.4776.8045.9276.331
Mar-965.6916.1446.4636.8685.8846.312
Apr-965.9405.9666.3056.8085.7426.193
May-966.1615.4935.7336.4095.2585.798
Jun-966.0135.4955.6356.2535.1495.647
Jul-966.1175.4295.7326.4835.2375.724
Aug-966.2315.5725.6836.2855.2155.716
Sep-966.0085.4995.6436.1625.1305.648
Oct-965.6685.1915.4906.0444.9225.479
Nov-965.5084.6745.2505.9784.6135.251
Dec-965.7904.9305.0925.6034.5225.089
Jan-975.8394.6074.9545.8264.4415.023
Feb-976.0085.1925.3296.1184.9715.436
Mar-976.3355.3775.6026.2585.1145.586
Apr-976.1935.4995.7956.3285.2695.712
May-976.1176.0016.0146.4445.6085.964
Jun-975.9915.7255.8926.3145.4425.833
Jul-975.6605.7806.0096.3945.5525.935
Aug-975.8745.8396.0996.5055.6246.003
Sep-975.7125.5635.8786.3355.3885.800
Oct-975.5675.4015.6246.1565.2075.632
Nov-975.7115.4195.4775.9285.1025.460
Dec-975.5785.6185.7206.1365.3425.726
Jan-985.2635.5765.7436.2075.3775.677
Feb-985.4695.7675.8716.2225.4805.799
Mar-985.5036.1066.1866.4555.7836.069
Apr-985.5095.7256.0236.2955.4865.876
May-985.4655.6355.9536.1905.3635.746
Jun-985.4045.6715.8516.1835.3495.770
Jul-985.4185.2715.5485.8974.9855.479
Aug-984.8145.7195.7986.0655.3385.747
Sep-984.2775.4805.6195.8245.1035.542
Oct-984.1675.2125.4525.7054.9375.373
Nov-984.4785.5045.5845.6725.1075.537
Dec-984.5195.3295.4925.6464.9945.427
Jan-994.5315.1295.2455.5204.8175.238
Feb-995.0975.2265.3995.5794.8825.277
Mar-994.9385.2195.4195.6054.9065.351
Apr-995.0115.4135.4275.4574.9645.404
May-995.3545.3355.4015.3354.9035.349
Jun-995.4564.8845.3145.3424.6725.138
Jul-995.5594.8675.3355.3364.6705.140
Aug-995.6504.5244.8865.0944.3394.776
Sep-995.5504.0164.3874.4163.7294.090
Oct-995.7233.9914.3754.7203.8214.238
Nov-995.9314.5384.6044.8074.1524.465
Dec-996.1484.4364.5954.7084.0754.448
Jan-006.5064.4754.5624.7014.0904.448
Feb-006.4414.7885.0435.1844.5364.831
Mar-006.3904.6484.9255.2574.4924.759
Apr-006.5674.8525.0025.2704.6214.921
May-006.5975.0185.2715.4114.8365.106
Jun-006.2805.3925.4165.5355.1055.348
Jul-006.2045.7565.5345.6285.3495.567
Aug-006.0875.4875.6375.6835.3005.517
Sep-005.8855.3735.5265.6135.2035.455
Oct-005.8245.5975.6835.6505.3945.666
Nov-005.5485.7235.8605.8365.5725.835
Dec-005.0516.0306.0706.0485.8376.081
Jan-014.5676.3616.3426.1476.0966.401
Feb-014.3866.3516.3106.0896.0946.443
Mar-014.1866.1426.2045.8425.9016.337
Apr-014.2786.4406.3495.7606.0526.531
May-014.2136.4146.3435.5225.9296.536
Jun-014.2336.1666.1835.7605.8526.293
Jul-013.7745.8686.1635.9565.7746.175
Aug-013.6095.9106.0265.8465.7296.101
Sep-012.8225.8185.9335.8745.6376.045
Oct-012.3705.8635.9175.9235.7005.947
Nov-012.8405.2985.6045.7195.3025.594
Dec-013.0664.7895.1855.5134.8915.134
Jan-023.1534.3664.7325.3824.4874.691
Feb-023.0444.4314.5885.3174.4604.591
Mar-023.6744.3914.3925.1914.3084.441
Apr-023.2164.4314.4895.3394.3634.666
May-023.1874.3564.3955.3034.2664.557
Jun-022.8754.1764.4195.3064.2034.527
Jul-022.2234.0554.0905.2314.0634.356
Aug-022.1094.0073.9555.0073.9244.105
Sep-021.6813.2493.3484.7493.4033.645
Oct-021.6653.3773.0074.5053.3273.462
Nov-022.0393.2123.2594.6723.2943.508
Dec-021.5823.2923.4214.8253.4203.634
Jan-031.6913.3303.4784.7763.4203.644
Feb-031.5103.4483.4014.6743.4383.621
Mar-031.4864.1493.9124.8513.9794.090
Apr-031.4773.6023.5474.7673.6923.817
May-031.3173.4303.4664.6893.6463.765
Jun-031.2993.2873.2554.6313.5293.631
Jul-031.7382.6752.8754.5993.1863.167
Aug-031.9612.3282.6844.2372.8823.010
Sep-031.4621.9132.2993.8272.4442.446
Oct-031.8211.9712.3384.0762.5402.411
Nov-032.0342.2952.5874.1152.7492.622
Dec-031.8392.2812.2593.8842.6182.481

Figure 15c. Observed and Predicted Yields, 12-Month Forecast Horizon: 5-Year Yield

Data for Figure 15c immediately follows.

Data for Figure 15c

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-945.0185.6835.9747.323#N/A#N/A
Feb-945.5874.9075.6607.059#N/A#N/A
Mar-946.2064.7195.6487.036#N/A#N/A
Apr-946.5924.5035.5777.076#N/A#N/A
May-946.7234.8795.6926.953#N/A#N/A
Jun-946.9214.7105.3796.559#N/A#N/A
Jul-946.6724.8425.4106.507#N/A#N/A
Aug-946.7544.3815.1176.233#N/A#N/A
Sep-947.2184.4055.0836.121#N/A#N/A
Oct-947.4124.4255.1226.129#N/A#N/A
Nov-947.6734.7295.4126.512#N/A#N/A
Dec-947.6744.8185.4016.4785.0104.818
Jan-957.4194.7265.2566.2614.8854.726
Feb-956.9615.2405.7156.6145.3345.240
Mar-956.9736.1226.2777.0636.0396.122
Apr-956.7676.4846.5577.1316.2896.484
May-955.9936.3386.6657.1566.2836.338
Jun-955.8946.6186.8287.2826.4476.757
Jul-956.0766.3496.6347.1586.2686.334
Aug-955.9856.5006.7277.2496.4026.518
Sep-955.9127.0497.1287.5156.8286.999
Oct-955.7267.1997.3097.6316.9857.179
Nov-955.4567.3927.4867.4977.0487.298
Dec-955.3077.3657.4587.1576.8657.139
Jan-965.1906.9647.2577.3496.7317.075
Feb-965.6676.6216.8957.2176.4786.850
Mar-966.0436.5666.9067.2776.4646.855
Apr-966.3206.3506.7587.2066.3136.731
May-966.5625.7266.1056.7245.7756.251
Jun-966.3795.6646.0326.5895.6746.133
Jul-966.4935.7476.2106.8685.8376.286
Aug-966.6365.7826.0906.6415.7736.196
Sep-966.3865.6646.0066.4945.6226.074
Oct-966.0075.3855.8376.3615.4215.910
Nov-965.7564.9405.6046.2565.1505.702
Dec-966.1435.0725.4345.9115.0325.519
Jan-976.1824.8835.4026.1675.0525.541
Feb-976.3185.5125.8616.5265.5985.971
Mar-976.6745.7376.1056.6755.7486.132
Apr-976.4925.9426.3446.7935.9406.287
May-976.4126.3736.5356.9196.2126.500
Jun-976.3086.1076.3906.7706.0416.354
Jul-975.8326.1756.4666.8336.1186.434
Aug-976.1306.2686.6056.9716.2256.535
Sep-975.9115.9856.3786.7895.9926.330
Oct-975.6335.7316.0646.5645.7756.127
Nov-975.7595.5945.8326.2855.5715.934
Dec-975.6325.9516.1446.5525.8796.197
Jan-985.3105.9326.1986.6315.9216.239
Feb-985.5126.0806.2806.6385.9796.296
Mar-985.5446.4326.6186.8996.3006.577
Apr-985.5626.0736.4356.7216.0156.305
May-985.4855.9616.3536.6225.8876.249
Jun-985.3855.9616.2506.5955.8316.194
Jul-985.4675.4485.8426.2285.4435.793
Aug-984.8655.8986.1266.4455.7446.044
Sep-984.3475.6355.9176.1885.5125.824
Oct-984.4805.2875.7106.0165.3035.644
Nov-984.5625.5245.7685.9575.3975.712
Dec-984.5915.3405.6435.9075.2705.613
Jan-994.5275.0685.4205.7745.0905.428
Feb-995.2065.1785.5395.8295.1385.492
Mar-995.1695.1985.5905.8715.1785.518
Apr-995.2665.3555.5975.7455.2155.512
May-995.6405.2705.5215.6015.1285.428
Jun-995.7594.9115.4285.5784.9255.283
Jul-995.9224.9735.4605.5864.9535.287
Aug-995.9684.5615.0295.3144.6254.970
Sep-995.8794.0214.4914.6143.9704.336
Oct-996.0454.1744.6084.9864.2034.543
Nov-996.1434.4464.7545.0354.3804.694
Dec-996.3904.3844.7394.9324.3214.633
Jan-006.6604.3464.7224.9254.3394.611
Feb-006.5694.8895.2795.4844.8505.107
Mar-006.2534.8275.2415.5924.8685.081
Apr-006.4565.0235.2945.6084.9775.204
May-006.4535.3325.5965.7765.2585.437
Jun-006.1585.6205.7085.9035.4865.598
Jul-006.1345.9455.8546.0305.7145.785
Aug-005.9325.7475.9196.0595.6725.768
Sep-005.7975.6535.8335.9865.6155.747
Oct-005.7065.8975.9516.0125.7315.886
Nov-005.3895.9536.0866.1645.8606.053
Dec-004.9896.2576.3156.3866.1296.323
Jan-014.8476.5326.5216.4576.3186.464
Feb-014.6996.4856.4306.3616.2856.432
Mar-014.6206.1306.1726.0105.9766.164
Apr-014.9386.4556.3125.9556.1046.237
May-014.9776.3456.2955.7435.9486.096
Jun-015.0676.1096.1185.9185.9326.105
Jul-014.6715.9556.0946.0715.8886.122
Aug-014.4975.8555.9175.9195.7916.026
Sep-014.0555.7865.8865.9805.7605.990
Oct-013.6755.7925.8365.9965.7726.002
Nov-014.1035.2885.5495.7685.4135.685
Dec-014.4474.8715.2165.5935.0925.379
Jan-024.5194.7435.0595.6414.9335.169
Feb-024.3584.8034.9265.5624.9225.086
Mar-025.0034.8164.8635.5334.8565.019
Apr-024.5845.0245.1285.8195.0475.231
May-024.4145.0585.1365.8485.0405.209
Jun-024.1495.0275.1685.8455.0395.221
Jul-023.6364.8434.8535.7494.9135.074
Aug-023.2844.7174.6815.5214.7354.889
Sep-022.6734.2754.3245.4094.4304.557
Oct-022.8764.2844.0285.1924.3444.385
Nov-023.3194.2204.4195.4784.4354.470
Dec-022.8094.4474.6565.7094.6344.664
Jan-033.0444.4784.6555.6274.6134.719
Feb-032.7264.4394.5245.4984.5674.588
Mar-032.8255.1215.0295.7225.0395.037
Apr-032.8874.6634.7075.6324.8344.820
May-032.3514.4254.6205.5344.7064.702
Jun-032.5014.2334.4155.4804.5894.571
Jul-033.3623.7094.0465.4254.2984.267
Aug-033.5133.2403.7514.9753.8973.880
Sep-032.8802.6313.3014.4953.3693.355
Oct-033.2962.8703.4594.8383.5683.550
Nov-033.3873.3423.7594.9443.8273.814
Dec-033.2643.1423.3814.6713.6163.594

Figure 15d. Observed and Predicted Yields, 12-Month Forecast Horizon: 10-Year Yield

Data for Figure 15d immediately follows.

Notes: The figure shows the observed yields for different maturities, together with the 12-month forecast from selected models. See Figure 12 for further details.

Data for Figure 15d

MonthObservedAR-XVAR-XNS2-ARFC-MSPE-XFC-MCS-MSPE
Jan-945.8506.6676.8197.726#N/A#N/A
Feb-946.2015.8506.4597.440#N/A#N/A
Mar-946.8735.7326.4337.419#N/A#N/A
Apr-947.1485.6746.4077.473#N/A#N/A
May-947.2345.8766.4267.317#N/A#N/A
Jun-947.4545.6046.0676.891#N/A#N/A
Jul-947.2815.6256.0686.834#N/A#N/A
Aug-947.2635.1435.7636.538#N/A#N/A
Sep-947.6785.1545.7126.424#N/A#N/A
Oct-947.8555.1625.7426.426#N/A#N/A
Nov-947.8565.5536.0866.838#N/A#N/A
Dec-947.7425.5726.0716.8105.6875.572
Jan-957.5605.4655.9116.5825.5425.465
Feb-957.1335.7796.3126.9335.8965.779
Mar-957.1996.7126.8877.4126.5706.712
Apr-957.1046.9667.0587.4486.7606.703
May-956.3296.8097.0907.4476.7156.695
Jun-956.2817.1017.2717.5896.9056.965
Jul-956.5446.8987.0987.4426.7476.822
Aug-956.3186.9497.1767.5166.8516.988
Sep-956.2027.4517.5407.7917.2297.430
Oct-956.0437.5917.6947.9007.3857.692
Nov-955.7187.5447.6687.6917.3147.654
Dec-955.5647.4037.4627.3017.0557.525
Jan-965.6057.0807.4297.5057.0097.561
Feb-966.1086.7387.1607.3736.7797.346
Mar-966.3236.7507.1967.4346.8067.391
Apr-966.6346.6527.0667.3616.7367.292
May-966.7875.9906.4416.8466.1646.787
Jun-966.6745.9836.3576.7186.0806.682
Jul-966.7496.1686.5927.0266.2886.880
Aug-966.9026.0536.4216.7816.1426.721
Sep-966.6785.8976.2966.6205.9866.460
Oct-966.3025.6486.1236.4825.8086.245
Nov-966.0145.1575.9226.3645.5436.052
Dec-966.3875.2635.6976.0275.3935.843
Jan-976.4805.2365.8036.3105.5095.944
Feb-976.4885.9176.2466.6976.0536.372
Mar-976.8275.9976.4576.8466.1316.476
Apr-976.6516.2506.6646.9836.3286.637
May-976.5936.5816.8527.1136.5366.802
Jun-976.4296.3786.6866.9546.3876.673
Jul-975.9626.4146.7427.0096.4396.730
Aug-976.2526.5236.9127.1606.5666.847
Sep-976.0356.2616.6856.9736.3416.650
Oct-975.7705.9886.3846.7306.1296.448
Nov-975.8085.7986.1206.4255.8776.186
Dec-975.6836.1536.4426.7176.1806.479
Jan-985.4916.1946.5186.8026.2386.522
Feb-985.5406.2166.5636.8026.2686.528
Mar-985.5746.5666.8877.0746.5696.830
Apr-985.6026.2186.6826.8866.2936.651
May-985.4616.1316.5756.7886.1776.556
Jun-985.3466.0656.5266.7556.1056.419
Jul-985.4195.5516.0816.3515.7086.008
Aug-985.0475.9916.3756.5906.0096.262
Sep-984.4435.7266.1266.3235.7526.041
Oct-984.6685.3845.9356.1275.5465.859
Nov-984.6645.5255.9406.0525.5915.880
Dec-984.5995.3365.8275.9935.4455.766
Jan-994.6245.1855.6555.8615.3495.647
Feb-995.2535.1605.7345.9125.3235.650
Mar-995.2315.1955.7905.9605.3775.685
Apr-995.3615.3645.7425.8415.4115.675
May-995.5125.2155.6165.6835.2765.549
Jun-995.7114.8495.5375.6485.0885.382
Jul-995.8314.9175.5345.6635.1135.426
Aug-995.8634.6905.1895.3844.8525.155
Sep-995.7924.0194.6254.6704.1554.480
Oct-995.9524.2844.8505.0834.4744.768
Nov-996.1414.4714.9555.1104.6164.881
Dec-996.3874.3404.8955.0024.5104.778
Jan-006.5574.3854.9124.9964.5394.767
Feb-006.2364.9175.4495.5885.0505.264
Mar-006.0474.8725.4975.7185.0915.307
Apr-006.0395.0955.5235.7345.1965.388
May-006.1165.2305.7555.9115.4135.613
Jun-005.9045.5755.8736.0405.6315.783
Jul-005.9135.8536.0476.1825.8365.951
Aug-005.5735.6516.0556.1975.7835.939
Sep-005.7035.5785.9846.1245.7235.872
Oct-005.6675.8196.0386.1415.8575.987
Nov-005.4105.9506.1716.2775.9966.137
Dec-005.0976.2476.4326.5046.2506.378
Jan-015.1626.4326.5826.5566.3786.519
Feb-014.8596.1846.4596.4436.2676.414
Mar-014.9195.9306.0886.0395.9736.139
Apr-015.3726.0656.1455.9886.0146.147
May-015.4366.0186.0485.7775.8586.007
Jun-015.4775.8565.9915.9385.8856.050
Jul-015.1665.7246.0216.0775.8846.098
Aug-014.8445.5025.8475.9075.7485.954
Sep-014.6825.6755.8525.9865.8166.013
Oct-014.3675.7145.8365.9895.8436.035
Nov-014.9115.2735.5595.7525.5165.745
Dec-015.2064.9295.3015.5985.2645.495
Jan-025.2055.0025.3125.7395.2445.442
Feb-024.9304.9105.2195.6585.2055.367
Mar-025.4605.0465.2215.6775.1975.343
Apr-025.1935.4015.5236.0275.4635.589
May-025.1875.4735.5686.0885.5025.606
Jun-024.9935.4235.5666.0815.4845.599
Jul-024.7165.3065.3565.9875.4095.512
Aug-024.2345.0345.1575.7575.1765.288
Sep-023.7514.8534.9715.7265.0125.098
Oct-024.1004.9104.7565.5314.9834.997
Nov-024.3055.0125.1135.8655.1285.169
Dec-023.9765.2135.3646.1335.3345.375
Jan-034.1375.1845.3026.0325.2755.320
Feb-033.8055.0175.1885.8925.1585.203
Mar-033.9485.5945.6206.1245.5885.577
Apr-034.0135.2875.3866.0435.4165.418
May-033.4835.2105.2945.9365.3475.301
Jun-033.6625.0565.1675.8935.2505.255
Jul-034.5904.7334.9155.8505.0595.109
Aug-034.5924.1544.5185.3534.5934.668
Sep-034.1223.6594.0744.8454.1004.137
Oct-034.4924.0054.3595.2464.3804.465
Nov-034.4584.2574.5915.3684.5564.563
Dec-034.4204.1794.2865.0904.3884.371

Footnotes

1.  We thank Torben Andersen, Martin Martens, Dagfinn Rime, and Daniel Thornton for helpful discussions and for providing detailed comments, as well as seminar participants at the Catholic University Leuven, Erasmus University Rotterdam, Federal Reserve Bank of New York, Federal Reserve Board, Norges Bank, the 2008 Infinity Conference, and the 27th International Symposium on Forecasting. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other employee of the Federal Reserve System, nor do they reflect the views of Norges Bank (the Central Bank of Norway). This paper is best viewed in color. An earlier draft of this paper circulated under the name "Predicting the Term Structure of Interest Rates: Incorporating Parameter Uncertainty, Model Uncertainty and Macroeconomic Information" which is available as a Tinbergen Institute Discussion Paper (07-028/4). Return to text

2.  Corresponding author; De Pooter is a staff economist in the Division of International Finance, Board of Governors of the Federal Reserve System, Washington, D.C. 20551, U.SA., Tel.: (202) 452-2264, fax: (202) 452-6424. E-mail addresses: michiel.d.depooter@frb.gov (M. De Pooter), francesco.ravazzolo@norges-bank.no (F. Ravazzolo), djvandijk@ese.eur.nl (D. van Dijk). Return to text

3.  Macro variables, however, mainly seem to help in capturing the dynamics of short and medium-term rates. Modelling long-term yields remains difficult. DaiPhilippon2006 show that fiscal policy can account for some of the unexplained long rate dynamics whereas DeWachterLyrio2006 show that long-run inflation expectations are important for modelling long-term bond yields. Return to text

4.  See also Bansal and Zhou (2002), Dai, Singleton, and Yang (2007), and the references contained therein. Return to text

5.  We kindly thank Robert Bliss for providing us with the unsmoothed Fama-Bliss forward rates and the programs to construct the spot rates. Return to text

6.  Using contemporaneous information may exaggerate the benefits of using macroeconomic information when forecasting yields. Note, however, that we would only be able to fully mimic the information available to the econometrician at the time of making any forecast if we would use vintage data. Croushore2006 discusses the use of vintage data and shows that data revisions can lead to an improvement in perceived forecastability. Here we use only revised final-vintage macroeconomic series, implying that this may affect our results as well. Return to text

7.  As a robustness check we also examined using additional factors, but the forecasting results were very similar. With fewer factors (one or two) we obtained worse results. Note that we made a somewhat ad hoc choice for the number of factors, based solely on how much of the variance each factor explains in the cross section of macro series. An alternative, and arguably better approach, would be to select the number, as well as which factors, by using information criteria or by selecting only factors that are judged to have predictive power for interest rates. Although certainly interesting, we leave this for future research. Ludvigson and Ng (2009) use such an approach to select their factors. One interesting difference resulting from their approach compared to ours is that they find that they need to include a stock market factor. In our sample, the 7th PCA factor is most related to stock market variables, but explains only 3% of the variance in the macro panel and hence does not make the cut to be included in our vector of macro factors that we incorporate in the models. Return to text

8.  Note again that "contemporaneous" here means that we use financial series recorded at time $ t$, whereas time $ t-1$ values are used for the remaining macro series, see Section 2.2 for further details. Return to text

9.  In a forecasting exercise using German zero-coupon yields, Hordahl, Tristani, Vestin (2006) show that term-structure information helps little in forecasting macroeconomic variables (more specifically (i) inflation and (ii) the output gap) which provides an argument for forecasting macro variables outside of term structure models. The authors note, however, that this might be due to the fact that their proposed macroeconomic model has an imperfect ability to describe the joint dynamics of German macroeconomic variables. On the other hand, Diebold, Rudebusch, and Aruoba (2006) and Ang, Dong, and Piazzesi (2007) do allow for bi-directional effects between macro variables and latent yield factors but both studies find that the causality from macro variables to yields is much stronger than vice versa. Return to text

10.  For both the AR and VAR models we examined the benefits of including more lags by analyzing AR($ p$) and VAR($ p$) models with $ p=2,\ldots,12$. We found that using multiple lags resulted in nearly identical forecasts compared to the AR(1) and VAR(1) models and these results are therefore not reported, nor are they included in the forecasting combination procedures in Sections 4 and 5. Return to text

11.  Note that because we model the observable macro factors in $ M_{t}$ with a VAR(3) model, we need to add both the first and second lag, $ M_{t-1}$ and $ M_{t-2}$, respectively, to the state vector in order to write the state equations in companion form. Return to text

12.  The macro factors are prevented from entering the measurement equations directly by only allowing the factor loadings of $ \beta_{t}$ to be non-zero in (9). Diebold, Rudebusch, and Aruoba (2006) impose this restriction to maintain the assumption that three factors are sufficient to describe interest rate dynamics. We follow Diebold, Rudebusch, and Aruoba (2006) here because relaxing this assumption would result in a substantial number of additional parameters. Return to text

13.  Contrary to the reduced-form affine model of Ang and Piazzesi (2003), Hordahl, Tristani, and Vestin (2006) use a structural affine model with macroeconomic variables in which the number of parameters can be kept down. They show that their model leads to better longer horizon interest rate forecasts than the Ang and Piazzesi (2003) model. These results indicate that instead of only imposing no-arbitrage restrictions, which is the case in affine models, imposing also structural equations seems to mitigate overparameterization. Return to text

14.  To address the Lucas Critique and to check the robustness of our results, we also repeated our analysis using a moving window of ten years. Although somewhat surprising perhaps, results were rather similar to the expanding window results which we discuss below. Return to text

15.  To try and keep the number of graphs down we only show Trace CSPE graphs here. Graphs for individual maturities are available upon request. Return to text

16.  Note that Figures 8 to 11 contain the same information for the 1994-2003 period as do Figures 4 to 7 do. However, the graphs differ because the CSPEs start at zero in 1989 and 1994, respectively. Return to text

17.  Note that whereas in Panels A and B of Tables 3 to 6 we report results for the Root MSPE, Timmermann (2006) argues that it is better to use the MSPE to construct model weights. We therefore use MSPE in this forecast combination scheme. Return to text

18.  We also implement this combination scheme with the Range and Deviation statistics as in Hansen, Lunde, and Nason (2003), as well as for a 90% confidence level. Results were very similar to marginally worse than the statistics we report in Panels C of Tables 3 to 6. Return to text

19.  Note that the MCS to compute the inclusion percentages in Tables 3 to 6 is based on an expanding window that starts in 1989:1, whereas the full-sample MCS results in those same tables are based on the sample 1994:1 - 2003:12. It can happen therefore that a model is included in the full-sample MCS, while at the same time it is hardly ever included in the expanding MCS trimming combination scheme, i.e. it has a percentage close to, or equal to, zero. Return to text


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