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A Non-Random Walk Revisited: Short- and Long-Term Memory in Asset Prices

Paul S. Eitelman and Justin T. Vitanza*

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publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.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:

In this paper, we test for short and long memory in asset prices across 44 emerging and industrialized economies. Using methodology from Lo and MacKinlay (1988) and Lo (1991), we find that markets with a poor Sharpe ratio are more likely to reject the random walk than better performing markets. We also make a methodological contribution. Contrary to the Baillie (1996) criticism, our long memory analysis suggests that the choice of a truncation lag is not as important as one might initially believe. Tests that reject the null hypothesis tend to do so across any reasonable choice in lag.

Keywords: Random walk, long-range dependence, equities, commodities, exchange rates

JEL classification: E30, G14



1.  Introduction

This paper reexamines the possibility of both short- and long-term memory in asset returns. In a weak-form efficient market, all information contained in historical prices is instantaneously reflected in the current market price. This effectively precludes the opportunity to earn abnormal returns through a trend trading approach. However, some investment strategies are still dedicated to the research and exploitation of price trends. Given the continued use of technical analysis in financial economics, the random walk hypothesis deserves further empirical analysis. A random walk test indicates the existence of intertemporal dependence at some chosen lag. A rejection of the random walk hypothesis implies that a trend in asset prices, or memory, exists.

We make two main contributions to the literature. Using a uniquely large dataset1 of commodities and stock market indices from 44 emerging and industrial economies, we are able to compare the behavior of international asset prices. We first perform a random walk test on each market over several lags. Next, we calculate the Sharpe ratio. A regression of a dummy variable indicating whether or not the random walk was rejected on the Sharpe ratio revealed that markets with poorer risk-adjusted returns are more likely to reject the random walk hypothesis. This finding suggests that contrarian investment strategies, which look for undervalued assets in depressed markets, may offer the prudent investor an opportunity to beat the returns of standard equity indices.

Second, we test for long memory in asset returns using the Modified Rescaled Range (R/S) statistic developed by Lo (1991). Some criticisms of this test cite that there is no optimal method for choosing a truncation lag. Although this criticism is theoretically valid, the results of our analysis suggest that the choice of a truncation lag often has little bearing on the significance of results. We find mixed evidence of long memory in international equity markets. Of the advaned markets, only Denmark, Japan, Norway, and Sweden exhibit long memory. In the U.S. dollar foreign exchange markets, regional factors appear to be at play. We find that four of the six Latin American currencies studied in this paper (Argentina, Brazil, Chile, and Colombia) show long memory, whereas we fail to reject the null hypothesis for every advanced market currency and for most countries across Emerging Asia, the Middle East, and Africa. Of the 22 commodities evaluated in this paper, only soybeans and cattle show signs of long memory.


1.1  A Brief History of Previous Literature

Financial time series analysis focuses on the intertemporal dependencies of asset prices. Early asset pricing models were based on the assumptions that returns are identically and independently distributed (iid) with a log-normal distribution. Mandelbrot (1963) was among the first to show that the normal distribution does not adequately capture the "fat tails", or leptokurtosis, of returns. Engle (1982) and Bollerslev (1986) then identified the presence of time-varying conditional volatility, or "volatility clustering", in daily equity returns with their AutoRegressive Conditional Heteroscedasticity (ARCH) class of models. Many subsequent studies have since confirmed these findings, and the assumption of iid-normal returns is now widely rejected in the literature.

The Random Walk Hypothesis posits that today's stock price is an unforecastable transformation of its previous value. Based on this argument, Malkiel (1973) and Sharpe (1991) conclude that passive, low cost index funds should outperform their actively managed counterparts by some function of the trading, administrative, and management expenses owed. More broadly, any effort to forecast asset prices that follow the random walk should be value-draining.

There is considerable debate among financial economists whether the random walk hypothesis holds. Early research into the random walk hypothesis assumed constant volatility in the residual term. Because of Engle's well-documented exposition on the conditional volatility of returns, a rejection of the random walk because of heteroscedasticity is of little interest. The more advanced Lo and MacKinlay (1988) heteroscedasticity-consistent methodology is invariant to ARCH processes.

Mandelbrot (1971) also discovered a new empirical property in the time series of asset prices: low frequency persistent temporal dependence (hereafter long memory). Long memory is commonly characterized by a slower-than-exponential rate of decay in the autocorrelation function. For example, Taylor (1986) and Ding, Granger and Engle (1993) found a hyperbolic rate of decay in the absolute value of asset returns. As pointed out in Lo (1991), long-term memory is troublesome because it is inconsistent with the continuous time stochastic processes employed in martingale methods for the pricing of options and futures contracts. Mandelbrot (1972) adapted a previously existing test to identify the presence of long memory. This test, rescaled range, was first introduced by the hydrologist Harold Hurst (1951) to identify long-term patterns in the discharge of the Nile River.

The rest of this paper is organized as follows: Section 2 describes the methodology and results for our short memory (random walk) analysis, as well as a discussion on the power of our chosen test statistic. Section 3 describes the methodology and results of our long memory analysis. Section 4 concludes our paper and discusses practical applications for our findings in financial economics. The appendices provide a more detailed view of our data and results.

2.  Short Memory

2.1  Methodology

First we denote $ P_{t}$ as the index level at time $ t$ and define the log-price process $ X_{t}\equiv$ ln$ P_{t}$. The conventional form of the random walk is then given as

$\displaystyle X_{t}=\mu+X_{t-1}+\epsilon_{t}$, (1)

where $ \mu$ is an arbitrary drift parameter, and $ \epsilon_{t}$ is the random error term. The standard null hypothesis, H$ _{0}$, stipulates that the error terms $ \epsilon_{t}$ are independently and identically distributed normal random variables with constant variance $ \sigma_{o}^{2}$, or
H$\displaystyle _{0}$$\displaystyle \epsilon_{t}$ IID $\displaystyle N(0,\sigma_{o}^{2})$. (2)

However, given the well-documented fact that financial time series deviate from normality,2 and the mounting evidence of volatility clustering shown first by Engle (1982) and Bollerslev (1986), a rejection of the random walk due to these factors would be of little interest. Therefore, we study the short memory processes of our variables using the Lo and MacKinlay (1988) variance ratio test. This test assumes that $ X_{t}$ possesses uncorrelated increments, but it allows for more general forms of heteroscedasticity and relaxes the requirement for Gaussian increments.

The rest follows almost directly from the Lo and MacKinlay methodology.3 For $ nq+1$ observations $ \left[ X_{0},X_{1},...,X_{nq}\right] $, where $ q$ is any integer greater than 1, we define the asymptotic estimators of the mean and variance of returns, respectively:

$\displaystyle \hat{\mu}\equiv\frac{1}{nq}\overset{nq}{\underset{k=1}{\sum}}(X_{k} -X_{k-1})=\frac{1}{nq}(X_{nq}-X_{0})$ (3)

$\displaystyle \bar{\sigma}_{a}^{2}=\frac{1}{nq-1}\underset{k=1}{\overset{nq}{ {\displaystyle\sum} }}(X_{k}-X_{k-1}-\hat{\mu})^{2}$ . (4)

We then define $ \bar{M}_{r}(q)$ as the variance ratio that obtains
$\displaystyle \bar{M}_{r}(q)\overset{a}{=}\overset{q-1}{\underset{j=1}{\text{ }\sum}} \frac{2(q-j)}{q}\hat{\rho}(j)\text{,}$ (5)

where $ \hat{\rho}(j)$ is the autocorrelation coefficient estimator. Note that when $ q=2$, $ \bar{M}_{r}(2)$ simplifies to the first-order autocorrelation coefficient, $ \hat{\rho}(1)$. Continuing from theorem 3 of Lo and MacKinlay (1988), we define $ \hat{\delta}(j)$ and $ \hat{\theta}(q)$ as the heteroscedasticity-consistent estimators of the asymptotic variances of $ \hat{\rho}(j)$ and $ \bar{M}_{r}(q)$, respectively
$\displaystyle \hat{\delta}(j)=\frac{nq\underset{k=j+1}{\overset{nq}{\sum}}(X_{k} -X_{k-1}-\hat{\mu})^{2}(X_{k-j}-X_{k-j-1}-\hat{\mu})^{2}}{\left[ \overset {nq}{\underset{k=1}{\sum}}(X_{k}-X_{k-1}-\hat{\mu})^{2}\right] ^{2}}$ (6)

$\displaystyle \hat{\theta}(q)\equiv\underset{j=1}{\overset{q-1}{\sum}}\left[ \frac {2(q-j)}{q}\right] ^{2}\hat{\delta}(j)$ . (7)

The following test statistic $ z^{\ast}(q)$ is asymptotically standard normal and is used to describe our empirical results in section 2.2. Note that q can be interpreted as the period for which the existence of memory is being tested.

$\displaystyle z^{\ast}(q)\equiv\frac{\sqrt{nq}\bar{M}_{r}(q)}{\sqrt{\hat{\theta}(q)} }\overset{a}{\sim}N(0,1)$ . (8)

This test statistic is ideal for evaluating the random walk hypothesis because it accounts for the volatility clustering inherent in asset prices. However, since the effective sample size decreases as $ q$ gets larger, small-sample biases will skew this statistic at sufficiently large lags (Lo and MacKinlay, 1989).

2.2  Results

The results of our random walk study are shown in Appendix 3. The dashed orange and red lines represent 95 and 99 percent rejection levels of the heteroscedasticity-consistent random walk hypothesis test, respectively. $ \ z $*-values significantly greater than zero imply a positive persistence in the autocorrelation function for the time series at some lag, $ q$; $ z$*-values below the lower rejection band show a mean-reversion in the time series at that lag. This paper does not attempt to prove explanatory factors for any non-random processes identified herein; instead we reveal those areas where further fundamental analysis should prove fruitful for academics and practitioners. A few notable themes emerge.

In commodity markets, we find common trends within commodity groupings. Energy items, including crude oil, natural gas, and heating oil, exhibit mean reverting price behavior. This finding is consistent with recent work by Geman (2007). As in Bleaney and Greenaway (1993), we fail to reject the random walk hypothesis for each of the nine metals series in our study. The agricultural raw materials, namely cotton and rubber, show significant persistence in returns while the finished farm products are largely random. Soybean prices are the exception, however, as they are shown to deviate from the random walk.

We fail to reject the random walk hypothesis for U.S. foreign exchange markets. Our findings are consistent with Liu and He (1991), who used the same heteroscedasticity-consistent methodology. We find that the Yen-Dollar and Pound-Dollar rates each exhibit positive serial correlation, particularly for small $ q$ values, whereas the random walk cannot be rejected for the Canadian-U.S. Dollar rate. Other notable currencies include the Australian dollar and the Euro, both of which seem to exhibit random price behavior.

We also fail to reject the random walk hypothesis for the S&P 500, a value-weighted index, at any conventional lag. Similarly, we cannot reject the random walk hypothesis for many other major international equity markets, including China, the United Kingdom, France, Germany, India, Brazil, Switzerland, South Korea, Spain, and Sweden. This is consistent with the findings of Campbell, Lo and MacKinlay (1997).4 They cannot reject the random walk hypothesis for a U.S. value-weighted index. However, the main finding of their paper is that they reject the random walk for the CRSP equal-weighted index. Accordingly, they suggest that firm size is a driving factor for the "randomness" of its security price. From our analysis, it appears that risk-adjusted returns are also an indicator of predictability. For example, by ordering markets according to their Sharpe ratios5, $ S=\frac{\mu}{\sigma}$, we notice that the seven weakest equity markets in our sample: Czech Republic, Philippines, Japan, Thailand, Italy, and Argentina, all reject the random walk. This result is supported by economic intuition. Low risk-adjusted returns should decrease the demand for analyst coverage, which would result in weaker informational efficiency.

In Figure 2.2.1, we show a scatterplot of the Sharpe ratio ($ S$) against the maximum value over all lags of the absolute value of $ z^{\ast}(q).$ The $ S$ was calculated using the return and standard deviation of returns over all available data. Sweden was immediately disregarded as an outlier.

Figure 2.2.1

Data for Figure 2.2.1 immediately follows

Data for Figure 2.2.1: Non-Oil

  Zmax Sharpe Ratio
Argentina
2.832
0.050
Brazil
0.697
0.126
Chile
6.145
0.139
Colombia
1.504
0.186
Mexico
1.881
0.139
Peru
4.131
0.158
China
1.944
0.070
Hong Kong
4.265
0.068
India
1.178
0.091
South Korea
2.060
0.055
Malaysia
2.530
0.055
Philippines
4.066
0.048
Russia
2.709
0.071
Singapore
3.769
0.064
Taiwan
3.963
0.049
Thailand
3.702
0.032
Israel
0.649
0.089
South Africa
1.153
0.106
Turkey
1.246
0.118
Australia
2.818
0.085
Belgium
0.943
0.076
Canada
2.811
0.090
Czech Republic
1.930
0.037
Denmark
2.234
0.107
France
2.063
0.064
Germany
1.802
0.074
Hungary
2.715
0.102
Italy
4.335
0.050
Japan
2.407
0.041
Netherlands
1.023
0.071
Norway
2.468
0.088
New Zealand
1.192
0.110
Poland
4.165
0.092
Spain
1.532
0.102
Switzerland
1.324
0.073
United Kingom
1.096
0.072
United States
0.896
0.089
Aluminum
1.669
0.168
Copper
0.950
0.113
Gold
0.940
0.158
Lead
1.742
0.089
Nickel
1.673
0.163
Platinum
2.468
0.112
Silver
0.815
0.167
Tin
1.066
0.181
Zinc
1.212
0.131
Cattle
1.978
0.051
Cocoa
5.905
0.159
Coffee
1.819
0.080
Corn
1.853
0.096
Cotton
2.802
0.093
Rubber
1.732
0.015
Soybeans
2.019
0.055
Sugar
1.178
0.106
Wheat
2.214
0.107

Data for Figure 2.2.1: Oil

  Zmax Sharpe Ratio
Indonesia
1.331
0.067
Kuwait
3.449
0.268
Nigeria
2.144
0.166
Saudi Arabia
3.045
0.082
UAE
10.077
0.190
Venezuela
3.205
0.124
Crude Oil
2.266
0.024
Natural Gas
1.459
0.066
Heating Oil
2.288
0.019
Gasoline
2.217
0.121

We immediately noticed that energy commodities and OPEC-member equity markets tended to deviate from the majority of the data. Removing these points magnifies the relationship between risk-adjusted performance and forecastability, as shown in Figure 2.2.2.

Figure 2.2.2

Data for Figure 2.2.2 immediately follows.  The equation for the fitted line is:max(|z*(q)|) = 2.577 - 3.798(S)

Data for Figure 2.2.2: Non-Oil

  Zmax Sharpe Ratio
Argentina
2.832
0.050
Brazil
0.697
0.126
Chile
6.145
0.139
Colombia
1.504
0.186
Mexico
1.881
0.139
Peru
4.131
0.158
China
1.944
0.070
Hong Kong
4.265
0.068
Indonesia
1.331
0.067
India
1.178
0.091
South Korea
2.060
0.055
Malaysia
2.530
0.055
Philippines
4.066
0.048
Russia
2.709
0.071
Singapore
3.769
0.064
Taiwan
3.963
0.049
Thailand
3.702
0.032
Israel
0.649
0.089
Nigeria
2.144
0.166
South Africa
1.153
0.106
Turkey
1.246
0.118
Australia
2.818
0.085
Belgium
0.943
0.076
Canada
2.811
0.090
Czech Republic
1.930
0.037
Denmark
2.234
0.107
France
2.063
0.064
Germany
1.802
0.074
Hungary
2.715
0.102
Italy
4.335
0.050
Japan
2.407
0.041
Netherlands
1.023
0.071
Norway
2.468
0.088
New Zealand
1.192
0.110
Poland
4.165
0.092
Spain
1.532
0.102
Switzerland
1.324
0.073
United Kingom
1.096
0.072
United States
0.896
0.089
Aluminum
1.669
0.168
Copper
0.950
0.113
Gold
0.940
0.158
Lead
1.742
0.089
Nickel
1.673
0.163
Platinum
2.468
0.112
Silver
0.815
0.167
Tin
1.066
0.181
Zinc
1.212
0.131
Cattle
1.978
0.051
Cocoa
5.905
0.159
Coffee
1.819
0.080
Corn
1.853
0.096
Cotton
2.802
0.093
Rubber
1.732
0.015
Soybeans
2.019
0.055
Sugar
1.178
0.106
Wheat
2.214
0.107

Table 2.2.1 shows the correlation between these series along with the coefficients and t-statistics of a regression of a dummy variable which indicates whether or not that market can reject the random walk with 95 confidence at some lag (i.e. $ \max(\vert z^{\ast}(q)\vert)>1.96$) on the $ S$. Though only the OLS estimates are reported, the results are robust to several modifications, including robust standard errors and iteratively reweighted least squares with Huber and biweight functions tuned to 95% efficiency.

Table 2.2.1

Assets Correlation $ (S,\max(\vert z^{\ast}(q)\vert))$ $ \mathbf{\beta}$ t-stat
Non-Oil $ -0.13$ $ -3.25$ $ -2.05$

This preliminary evidence supports our hypothesis that there exists a positive relationship between risk-adjusted market performance and efficiency. Further research in this area would likely prove rewarding.

2.3  Power

In this section, we detail the relative power of the Lo and MacKinlay (1988) heteroscedasticity-consistent random walk test compared to the more restrictive random walk under homoscedastic increments. One should expect that, for random asset price innovations, both the homoscedastic and heteroscedastic methodologies will fail to reject the null hypothesis of a random walk and produce very similar results. Our simulation results confirm this. As an example, we include the first sample of the simulation in Figure 2.3.1.

Figure 2.3.1  IID-Normal Process

Data for Figure 2.3.1 immediately follows

Data for Figure 2.3.1

The 95% critical values are plus-or-minus 1.96, and the 99% critical values are plus-or-minus 2.58. The critical values do not depend upon q.

q Heteroscedastic Test - zHomoscedastic Test - z
20.3525 0.3359
30.0054 0.0053
40.1036 0.1007
50.1968 0.1913
60.0716 0.0695
70.0979 0.0951
80.1497 0.1455
90.1839 0.1788
100.3196 0.3108
110.5123 0.4986
120.6368 0.6201
130.7741 0.7543
140.9282 0.9051
150.9984 0.9741
161.067 1.0415
171.153 1.1259
181.1982 1.1705
191.2584 1.2297
201.3096 1.2801
211.3671 1.3367
221.4003 1.3695
231.4225 1.3917
241.4097 1.3796
251.3973 1.3679
261.3619 1.3338
271.3196 1.2928
281.2664 1.2411
291.2283 1.204
301.1806 1.1576
311.1354 1.1136
321.0804 1.0599
331.0065 0.9876
340.9376 0.9202
350.8609 0.845
360.7751 0.761
370.6879 0.6754
380.6099 0.5989
390.5359 0.5262
400.4598 0.4516
410.3894 0.3824
420.3189 0.3133
430.2428 0.2385
440.1653 0.1623
450.0829 0.0814
460.0085 0.0084
47-0.0566 -0.0556
48-0.1214 -0.1193
49-0.1746 -0.1715
50-0.2181 -0.2143
51-0.2655 -0.2609
52-0.313 -0.3075
53-0.3577 -0.3515
54-0.3968 -0.3899
55-0.436 -0.4284
56-0.4679 -0.4597
57-0.4996 -0.4909
58-0.5262 -0.517
59-0.5445 -0.535
60-0.5626 -0.5528
61-0.5827 -0.5726
62-0.597 -0.5866
63-0.6153 -0.6045
64-0.6401 -0.6289
65-0.6596 -0.648
66-0.6736 -0.6617
67-0.6871 -0.675
68-0.696 -0.6837
69-0.7108 -0.6982
70-0.7274 -0.7145
71-0.7369 -0.7238
72-0.7452 -0.732
73-0.7577 -0.7442
74-0.7686 -0.7549
75-0.7784 -0.7645
76-0.7919 -0.7777
77-0.8006 -0.7863
78-0.8094 -0.7948
79-0.8232 -0.8084
80-0.8377 -0.8226
81-0.8546 -0.8391
82-0.8721 -0.8563
83-0.8904 -0.8743
84-0.9053 -0.8888
85-0.9211 -0.9043
86-0.9378 -0.9207
87-0.9542 -0.9367
88-0.9677 -0.9499
89-0.9787 -0.9607
90-0.9872 -0.969
91-0.9989 -0.9804
92-1.0098 -0.9911
93-1.021 -1.0019
94-1.0332 -1.0139
95-1.0457 -1.0261
96-1.0588 -1.0389
97-1.0693 -1.0491
98-1.077 -1.0566
99-1.0837 -1.0631
100-1.0901 -1.0693
101-1.0978 -1.0768
102-1.1037 -1.0825
103-1.1094 -1.0881
104-1.1142 -1.0928
105-1.1135 -1.092
106-1.1154 -1.0937
107-1.1184 -1.0966
108-1.1185 -1.0966
109-1.1217 -1.0997
110-1.1234 -1.1013
111-1.1247 -1.1025
112-1.1243 -1.102
113-1.1255 -1.1031
114-1.1259 -1.1034
115-1.1282 -1.1055
116-1.1327 -1.1099
117-1.1343 -1.1114
118-1.1337 -1.1107
119-1.1311 -1.1081
120-1.1276 -1.1046
121-1.1246 -1.1016
122-1.1237 -1.1006
123-1.1207 -1.0976
124-1.1189 -1.0957
125-1.1156 -1.0925
126-1.1101 -1.087
127-1.1058 -1.0826
128-1.101 -1.0779
129-1.0941 -1.071
130-1.0861 -1.0631
131-1.0798 -1.0569
132-1.0727 -1.0499
133-1.0677 -1.0448
134-1.064 -1.0411
135-1.0608 -1.0379
136-1.058 -1.0351
137-1.0566 -1.0337
138-1.0552 -1.0322
139-1.0528 -1.0298
140-1.0537 -1.0306
141-1.0511 -1.028
142-1.0464 -1.0233
143-1.0429 -1.0198
144-1.0419 -1.0187
145-1.0396 -1.0164
146-1.0381 -1.0149
147-1.0379 -1.0146
148-1.0385 -1.0151
149-1.0403 -1.0167
150-1.0432 -1.0195
151-1.046 -1.0222
152-1.0484 -1.0244
153-1.0497 -1.0256
154-1.0504 -1.0262
155-1.0523 -1.028
156-1.0544 -1.0299
157-1.0567 -1.0321
158-1.0563 -1.0316
159-1.0561 -1.0313
160-1.0563 -1.0314
161-1.0572 -1.0323
162-1.0591 -1.034
163-1.06 -1.0348
164-1.0593 -1.034
165-1.0581 -1.0328
166-1.0588 -1.0334
167-1.0592 -1.0337
168-1.0606 -1.0349
169-1.06 -1.0343
170-1.0595 -1.0337
171-1.059 -1.0331
172-1.0591 -1.0331
173-1.0594 -1.0333
174-1.0585 -1.0323
175-1.0573 -1.0311
176-1.0571 -1.0308
177-1.0566 -1.0302
178-1.0552 -1.0288
179-1.0527 -1.0263
180-1.0509 -1.0245
181-1.0486 -1.0221
182-1.0463 -1.0197
183-1.0446 -1.018
184-1.0416 -1.015
185-1.0384 -1.0118
186-1.0375 -1.0108
187-1.038 -1.0113
188-1.0386 -1.0118
189-1.0397 -1.0127
190-1.0411 -1.014
191-1.0411 -1.0139
192-1.0412 -1.0138
193-1.0415 -1.0141
194-1.042 -1.0145
195-1.0424 -1.0148
196-1.0439 -1.0162
197-1.0446 -1.0167
198-1.0465 -1.0185
199-1.0471 -1.019
200-1.0465 -1.0184
201-1.0455 -1.0172
202-1.0455 -1.0172
203-1.0455 -1.0171
204-1.0471 -1.0185
205-1.0498 -1.0211
206-1.0526 -1.0237
207-1.0566 -1.0276
208-1.0616 -1.0323
209-1.0651 -1.0355
210-1.0691 -1.0394
211-1.0725 -1.0426
212-1.0743 -1.0443
213-1.0759 -1.0457
214-1.0791 -1.0487
215-1.0826 -1.0521
216-1.0858 -1.055
217-1.0878 -1.0569
218-1.0889 -1.0579
219-1.089 -1.0579
220-1.0894 -1.0581
221-1.0892 -1.0579
222-1.0891 -1.0576
223-1.0893 -1.0577
224-1.0892 -1.0576
225-1.0885 -1.0567
226-1.0872 -1.0554
227-1.086 -1.0542
228-1.0843 -1.0524
229-1.0812 -1.0493
230-1.0773 -1.0454
231-1.0731 -1.0412
232-1.069 -1.0372
233-1.0657 -1.0339
234-1.0616 -1.0298
235-1.0572 -1.0254
236-1.0515 -1.0198
237-1.045 -1.0134
238-1.0384 -1.0068
239-1.0313 -0.9999
240-1.0239 -0.9926
241-1.0164 -0.9853
242-1.0098 -0.9788
243-1.0032 -0.9722
244-0.996 -0.9652
245-0.9887 -0.958
246-0.9812 -0.9507
247-0.9729 -0.9425
248-0.9646 -0.9344
249-0.9561 -0.9261
250-0.948 -0.9182
251-0.9418 -0.912
252-0.9361 -0.9065
253-0.9308 -0.9013
254-0.9259 -0.8964
255-0.9212 -0.8917
256-0.9159 -0.8865
257-0.9114 -0.8821
258-0.9067 -0.8775
259-0.9031 -0.8739
260-0.9004 -0.8712
261-0.8976 -0.8683
262-0.8953 -0.8661
263-0.8949 -0.8655
264-0.8958 -0.8663
265-0.8973 -0.8677
266-0.8987 -0.869
267-0.9013 -0.8714
268-0.9041 -0.874
269-0.9074 -0.8771
270-0.9108 -0.8803
271-0.9142 -0.8835
272-0.9189 -0.888
273-0.9238 -0.8926
274-0.9289 -0.8974
275-0.9343 -0.9026
276-0.9392 -0.9072
277-0.9452 -0.9129
278-0.9517 -0.919
279-0.9585 -0.9255
280-0.9654 -0.9321
281-0.9724 -0.9387
282-0.9783 -0.9444
283-0.9832 -0.949
284-0.9895 -0.9549
285-0.9953 -0.9604
286-1.0003 -0.9651
287-1.0048 -0.9694
288-1.0094 -0.9737
289-1.0134 -0.9775
290-1.0178 -0.9816
291-1.0218 -0.9854
292-1.0244 -0.9878
293-1.027 -0.9902
294-1.0288 -0.9918
295-1.0304 -0.9932
296-1.0314 -0.9941
297-1.0322 -0.9947
298-1.0324 -0.9948
299-1.0333 -0.9956
300-1.0342 -0.9963
301-1.0335 -0.9955
302-1.0323 -0.9943
303-1.0313 -0.9932
304-1.0302 -0.992
305-1.0293 -0.991
306-1.0278 -0.9895
307-1.0256 -0.9873
308-1.0236 -0.9852
309-1.0224 -0.984
310-1.0212 -0.9827
311-1.0205 -0.9819
312-1.0205 -0.9818
313-1.0196 -0.9808
314-1.0194 -0.9806
315-1.0193 -0.9803
316-1.019 -0.9799
317-1.0182 -0.9791
318-1.0181 -0.9789
319-1.0181 -0.9787
320-1.0179 -0.9785
321-1.0187 -0.9791
322-1.0191 -0.9793
323-1.0196 -0.9798
324-1.0207 -0.9807
325-1.0216 -0.9814
326-1.0213 -0.981
327-1.0218 -0.9814
328-1.0223 -0.9818
329-1.0231 -0.9824
330-1.0241 -0.9833
331-1.0251 -0.9841
332-1.0262 -0.9851
333-1.0279 -0.9865
334-1.0307 -0.9891
335-1.0326 -0.9908
336-1.034 -0.9921
337-1.0345 -0.9924
338-1.0346 -0.9924
339-1.035 -0.9926
340-1.0343 -0.9918
341-1.0327 -0.9902
342-1.0305 -0.988
343-1.0291 -0.9865
344-1.0279 -0.9852
345-1.0267 -0.984
346-1.0256 -0.9828
347-1.0247 -0.9818
348-1.0234 -0.9805
349-1.022 -0.979
350-1.0201 -0.977
351-1.0183 -0.9753
352-1.0161 -0.973
353-1.0133 -0.9702
354-1.0107 -0.9677
355-1.0082 -0.9651
356-1.0064 -0.9633
357-1.0038 -0.9606
358-1.0016 -0.9584
359-0.9986 -0.9554
360-0.9966 -0.9534
361-0.9944 -0.9512
362-0.9915 -0.9484
363-0.9892 -0.9459
364-0.9867 -0.9434
365-0.984 -0.9408
366-0.981 -0.9379
367-0.9787 -0.9355
368-0.9753 -0.9321
369-0.9721 -0.929
370-0.969 -0.9259
371-0.9661 -0.923
372-0.9626 -0.9195
373-0.9598 -0.9168
374-0.9571 -0.9141
375-0.9542 -0.9112
376-0.9514 -0.9084
377-0.9489 -0.9059
378-0.9465 -0.9035
379-0.9437 -0.9007
380-0.941 -0.898
381-0.9381 -0.8951
382-0.9351 -0.8922
383-0.933 -0.89
384-0.9305 -0.8876
385-0.9283 -0.8854
386-0.9264 -0.8834
387-0.9247 -0.8817
388-0.9233 -0.8802
389-0.9214 -0.8783
390-0.9188 -0.8758
391-0.9169 -0.8739
392-0.9149 -0.8718
393-0.9132 -0.87
394-0.9107 -0.8676
395-0.9081 -0.865
396-0.9054 -0.8623
397-0.9031 -0.8601
398-0.9016 -0.8585
399-0.9006 -0.8574
400-0.8996 -0.8563
401-0.8996 -0.8562
402-0.8992 -0.8558
403-0.8989 -0.8554
404-0.8987 -0.8551
405-0.8984 -0.8547
406-0.8989 -0.8551
407-0.8993 -0.8554
408-0.9004 -0.8563
409-0.9016 -0.8573
410-0.9022 -0.8578
411-0.9029 -0.8583
412-0.9038 -0.859
413-0.9049 -0.86
414-0.9056 -0.8605
415-0.9063 -0.8611
416-0.9071 -0.8618
417-0.909 -0.8634
418-0.9119 -0.8661
419-0.9141 -0.8681
420-0.917 -0.8707
421-0.9198 -0.8732
422-0.9239 -0.8771
423-0.928 -0.8808
424-0.9315 -0.884
425-0.9346 -0.8869
426-0.939 -0.8909
427-0.9426 -0.8942
428-0.9461 -0.8974
429-0.9483 -0.8994
430-0.9502 -0.9011
431-0.9524 -0.903
432-0.9535 -0.904
433-0.9541 -0.9045
434-0.9555 -0.9056
435-0.9566 -0.9065
436-0.9578 -0.9076
437-0.9584 -0.908
438-0.9597 -0.9091
439-0.9606 -0.9098
440-0.9625 -0.9116
441-0.9647 -0.9135
442-0.9667 -0.9153
443-0.9686 -0.917
444-0.9703 -0.9184
445-0.9712 -0.9192
446-0.9711 -0.919
447-0.9706 -0.9184
448-0.9702 -0.9179
449-0.9694 -0.9171
450-0.9695 -0.917
451-0.9699 -0.9172
452-0.9702 -0.9174
453-0.97 -0.9171
454-0.9703 -0.9173
455-0.9701 -0.9169
456-0.9695 -0.9163
457-0.9686 -0.9153
458-0.9675 -0.9142
459-0.9662 -0.9128
460-0.9647 -0.9112
461-0.9631 -0.9096
462-0.9619 -0.9083
463-0.9604 -0.9069
464-0.9585 -0.9049
465-0.9558 -0.9023
466-0.9529 -0.8994
467-0.9503 -0.8968
468-0.9474 -0.894
469-0.9441 -0.8907
470-0.9408 -0.8875
471-0.9382 -0.8849
472-0.9358 -0.8826
473-0.9336 -0.8804
474-0.9317 -0.8784
475-0.9294 -0.8762
476-0.9271 -0.8739
477-0.9245 -0.8714
478-0.9227 -0.8695
479-0.9211 -0.8679
480-0.9194 -0.8662
481-0.9173 -0.864
482-0.9155 -0.8622
483-0.9142 -0.8609
484-0.913 -0.8597
485-0.9113 -0.858
486-0.9091 -0.8557
487-0.9071 -0.8537
488-0.9053 -0.852
489-0.9039 -0.8505
490-0.9025 -0.8491
491-0.9018 -0.8483
492-0.9011 -0.8475
493-0.901 -0.8473
494-0.9007 -0.847
495-0.9011 -0.8472
496-0.9026 -0.8485
497-0.9039 -0.8496
498-0.9051 -0.8506
499-0.9063 -0.8516
500-0.9076 -0.8528

It is less obvious how the random walk tests will behave in the presence of time-varying volatility. Under GARCH(1,1) processes, the heteroscedasticity-consistent random walk test employed in this paper is shown to be robust to time-varying volatility and appropriately fails to reject the random walk, whereas the homoscedastic alternative is biased towards rejection. Figure 2.3.2 shows the first sample in our simulation and the rejection bias of the homoscedastic test.

Figure 2.3.2  GARCH(1,1) Process

Data for Figure 2.3.2 immediately follows

Data for Figure 2.3.2

The 95% critical values are plus-or-minus 1.96, and the 99% critical values are plus-or-minus 2.58. The critical values do not depend upon q.

q Heteroscedastic Test - zHomoscedastic Test - z
21.3891 2.2013
31.0473 1.7368
41.0384 1.7609
50.8409 1.4337
60.581 0.9905
70.4987 0.849
80.4899 0.8321
90.5269 0.8926
100.5798 0.9796
110.6094 1.0269
120.5921 0.9951
130.5591 0.937
140.5276 0.8816
150.4889 0.8145
160.4127 0.6855
170.329 0.5451
180.267 0.4411
190.2221 0.3658
200.1918 0.3152
210.1822 0.2986
220.1677 0.2743
230.1259 0.2055
240.0816 0.1329
250.0265 0.0432
26-0.039 -0.0633
27-0.087 -0.1411
28-0.1253 -0.2028
29-0.1585 -0.2562
30-0.1716 -0.277
31-0.1792 -0.289
32-0.1934 -0.3115
33-0.2229 -0.3586
34-0.2567 -0.4125
35-0.2889 -0.4636
36-0.3166 -0.5076
37-0.3407 -0.5457
38-0.3476 -0.556
39-0.354 -0.5657
40-0.3642 -0.5814
41-0.3772 -0.6015
42-0.4069 -0.6481
43-0.4398 -0.6999
44-0.4699 -0.7469
45-0.5004 -0.7946
46-0.5303 -0.8414
47-0.548 -0.8686
48-0.5693 -0.9015
49-0.5915 -0.9358
50-0.6093 -0.963
51-0.6346 -1.0021
52-0.6671 -1.0526
53-0.6881 -1.0847
54-0.7074 -1.1142
55-0.7297 -1.1484
56-0.7506 -1.1803
57-0.7664 -1.2042
58-0.7775 -1.2206
59-0.7805 -1.2243
60-0.7801 -1.2228
61-0.7765 -1.216
62-0.7738 -1.2108
63-0.7782 -1.2168
64-0.7809 -1.22
65-0.7856 -1.2263
66-0.7859 -1.2257
67-0.7834 -1.2207
68-0.7814 -1.2167
69-0.7845 -1.2204
70-0.788 -1.2248
71-0.7931 -1.2316
72-0.7984 -1.2387
73-0.8015 -1.2425
74-0.8039 -1.245
75-0.8067 -1.2483
76-0.8068 -1.2472
77-0.8046 -1.2427
78-0.8031 -1.2391
79-0.802 -1.2363
80-0.8022 -1.2355
81-0.8052 -1.2389
82-0.8076 -1.2413
83-0.8107 -1.245
84-0.8119 -1.2456
85-0.8149 -1.2488
86-0.8179 -1.2522
87-0.8215 -1.2564
88-0.8298 -1.2678
89-0.8397 -1.2816
90-0.8471 -1.2916
91-0.8568 -1.305
92-0.8675 -1.32
93-0.8737 -1.3279
94-0.8796 -1.3356
95-0.8854 -1.3429
96-0.8881 -1.3456
97-0.8911 -1.3486
98-0.8952 -1.3534
99-0.8995 -1.3584
100-0.9054 -1.3658
101-0.9123 -1.3748
102-0.9184 -1.3823
103-0.9229 -1.3875
104-0.928 -1.3937
105-0.9344 -1.4018
106-0.9404 -1.4092
107-0.9447 -1.414
108-0.9519 -1.4232
109-0.9607 -1.4346
110-0.9674 -1.443
111-0.9732 -1.45
112-0.9777 -1.455
113-0.9828 -1.4609
114-0.9892 -1.4687
115-0.9988 -1.4813
116-1.0093 -1.495
117-1.0205 -1.51
118-1.0295 -1.5215
119-1.0347 -1.5273
120-1.0357 -1.5271
121-1.0392 -1.5303
122-1.0418 -1.5323
123-1.0427 -1.5318
124-1.0432 -1.5307
125-1.0418 -1.5269
126-1.0384 -1.5201
127-1.0353 -1.5137
128-1.0323 -1.5076
129-1.0293 -1.5014
130-1.0258 -1.4945
131-1.023 -1.4886
132-1.0197 -1.4821
133-1.0164 -1.4755
134-1.0144 -1.4708
135-1.013 -1.467
136-1.0104 -1.4615
137-1.0077 -1.4558
138-1.006 -1.4517
139-1.0036 -1.4464
140-1.0019 -1.4423
141-1.0001 -1.4378
142-0.9968 -1.4314
143-0.9928 -1.424
144-0.9894 -1.4173
145-0.9854 -1.4099
146-0.9822 -1.4036
147-0.9796 -1.3983
148-0.9781 -1.3944
149-0.9769 -1.391
150-0.9761 -1.3882
151-0.9745 -1.3842
152-0.9717 -1.3786
153-0.9687 -1.3727
154-0.9656 -1.3666
155-0.9625 -1.3606
156-0.9603 -1.3559
157-0.959 -1.3525
158-0.9576 -1.3489
159-0.9561 -1.345
160-0.9549 -1.3418
161-0.954 -1.3389
162-0.9534 -1.3365
163-0.9535 -1.335
164-0.9535 -1.3335
165-0.9527 -1.3306
166-0.953 -1.3295
167-0.9542 -1.3296
168-0.955 -1.3291
169-0.9554 -1.3281
170-0.956 -1.3274
171-0.9566 -1.3266
172-0.9559 -1.324
173-0.9556 -1.3222
174-0.9555 -1.3204
175-0.9561 -1.3197
176-0.9573 -1.3198
177-0.9578 -1.3189
178-0.9572 -1.3165
179-0.9565 -1.314
180-0.956 -1.3119
181-0.9549 -1.3088
182-0.9535 -1.3054
183-0.9521 -1.3019
184-0.9506 -1.2984
185-0.9482 -1.2936
186-0.9463 -1.2895
187-0.9447 -1.2858
188-0.9429 -1.2819
189-0.9401 -1.2767
190-0.9377 -1.272
191-0.9351 -1.2669
192-0.9325 -1.262
193-0.9306 -1.258
194-0.9294 -1.2549
195-0.9275 -1.2509
196-0.9259 -1.2473
197-0.9241 -1.2435
198-0.9229 -1.2405
199-0.9219 -1.2377
200-0.9205 -1.2345
201-0.919 -1.2311
202-0.918 -1.2284
203-0.9173 -1.226
204-0.9167 -1.2239
205-0.9162 -1.2218
206-0.9152 -1.2192
207-0.9142 -1.2165
208-0.9135 -1.2143
209-0.9126 -1.2117
210-0.912 -1.2095
211-0.9115 -1.2075
212-0.9104 -1.2049
213-0.909 -1.2017
214-0.908 -1.199
215-0.9078 -1.1975
216-0.9078 -1.1961
217-0.9073 -1.1942
218-0.9069 -1.1923
219-0.9065 -1.1905
220-0.9062 -1.1889
221-0.906 -1.1874
222-0.9061 -1.1862
223-0.9065 -1.1855
224-0.9065 -1.1842
225-0.9062 -1.1826
226-0.9062 -1.1813
227-0.9068 -1.1809
228-0.9069 -1.1798
229-0.9066 -1.1781
230-0.9059 -1.176
231-0.9047 -1.1733
232-0.9039 -1.171
233-0.9034 -1.1691
234-0.9023 -1.1664
235-0.9007 -1.1632
236-0.899 -1.1598
237-0.8962 -1.1551
238-0.8933 -1.1501
239-0.8901 -1.1448
240-0.8873 -1.1401
241-0.8838 -1.1343
242-0.8802 -1.1286
243-0.8764 -1.1226
244-0.8726 -1.1166
245-0.868 -1.1096
246-0.8631 -1.1023
247-0.8574 -1.0939
248-0.8517 -1.0856
249-0.846 -1.0771
250-0.8404 -1.069
251-0.8352 -1.0614
252-0.8308 -1.0547
253-0.8266 -1.0484
254-0.8231 -1.0428
255-0.8192 -1.0369
256-0.8154 -1.0311
257-0.8116 -1.0254
258-0.8079 -1.0196
259-0.8044 -1.0142
260-0.8009 -1.0088
261-0.7972 -1.0033
262-0.7937 -0.9979
263-0.791 -0.9935
264-0.7889 -0.99
265-0.7871 -0.9868
266-0.7852 -0.9834
267-0.7838 -0.9808
268-0.7825 -0.9781
269-0.781 -0.9754
270-0.7799 -0.9731
271-0.7787 -0.9707
272-0.7784 -0.9694
273-0.7782 -0.9682
274-0.7783 -0.9675
275-0.7786 -0.9669
276-0.7784 -0.9658
277-0.7787 -0.9653
278-0.7789 -0.9647
279-0.7792 -0.9641
280-0.7803 -0.9646
281-0.7817 -0.9655
282-0.7834 -0.9667
283-0.7844 -0.967
284-0.786 -0.9681
285-0.7881 -0.9699
286-0.7899 -0.9712
287-0.7915 -0.9722
288-0.7932 -0.9735
289-0.7945 -0.9743
290-0.7963 -0.9756
291-0.7979 -0.9767
292-0.7996 -0.9779
293-0.8014 -0.9792
294-0.803 -0.9803
295-0.8038 -0.9805
296-0.8041 -0.98
297-0.8044 -0.9795
298-0.8052 -0.9796
299-0.8065 -0.9803
300-0.8076 -0.9808
301-0.8084 -0.9809
302-0.8083 -0.9799
303-0.8078 -0.9786
304-0.8071 -0.9768
305-0.8053 -0.9739
306-0.8031 -0.9703
307-0.8008 -0.9667
308-0.7986 -0.9633
309-0.7971 -0.9606
310-0.796 -0.9585
311-0.7948 -0.9563
312-0.7931 -0.9534
313-0.7904 -0.9494
314-0.7876 -0.9452
315-0.7851 -0.9414
316-0.7824 -0.9374
317-0.7805 -0.9344
318-0.7793 -0.9321
319-0.7787 -0.9307
320-0.7785 -0.9297
321-0.7786 -0.9291
322-0.7778 -0.9274
323-0.777 -0.9256
324-0.7756 -0.9233
325-0.7744 -0.921
326-0.7729 -0.9186
327-0.772 -0.9168
328-0.7711 -0.9149
329-0.7705 -0.9135
330-0.7701 -0.9122
331-0.7691 -0.9104
332-0.7679 -0.9082
333-0.7666 -0.906
334-0.7655 -0.904
335-0.7637 -0.9011
336-0.7618 -0.8982
337-0.7602 -0.8956
338-0.7588 -0.8933
339-0.758 -0.8916
340-0.7571 -0.8899
341-0.756 -0.8879
342-0.7546 -0.8856
343-0.7536 -0.8838
344-0.7531 -0.8825
345-0.7532 -0.8819
346-0.7534 -0.8814
347-0.754 -0.8815
348-0.7541 -0.8809
349-0.7541 -0.8802
350-0.7537 -0.8791
351-0.7537 -0.8785
352-0.753 -0.8771
353-0.7526 -0.8759
354-0.7521 -0.8746
355-0.7523 -0.8742
356-0.7529 -0.8743
357-0.753 -0.8737
358-0.7532 -0.8734
359-0.7527 -0.8722
360-0.7518 -0.8705
361-0.7506 -0.8685
362-0.748 -0.8648
363-0.7458 -0.8616
364-0.7431 -0.8579
365-0.7401 -0.8538
366-0.7369 -0.8495
367-0.7342 -0.8457
368-0.731 -0.8415
369-0.7278 -0.8372
370-0.7243 -0.8326
371-0.721 -0.8282
372-0.7176 -0.8236
373-0.7149 -0.82
374-0.7131 -0.8174
375-0.7113 -0.8147
376-0.7098 -0.8124
377-0.7084 -0.8102
378-0.7069 -0.8079
379-0.7047 -0.8049
380-0.7017 -0.8009
381-0.6984 -0.7966
382-0.6954 -0.7926
383-0.6927 -0.7889
384-0.69 -0.7853
385-0.6874 -0.7818
386-0.6849 -0.7785
387-0.6827 -0.7754
388-0.6799 -0.7717
389-0.6768 -0.7677
390-0.6739 -0.7639
391-0.6714 -0.7606
392-0.6691 -0.7574
393-0.6668 -0.7543
394-0.664 -0.7506
395-0.6613 -0.747
396-0.6589 -0.7438
397-0.6565 -0.7407
398-0.6541 -0.7375
399-0.6516 -0.7342
400-0.6491 -0.7309
401-0.6474 -0.7284
402-0.6464 -0.7269
403-0.6459 -0.7258
404-0.6459 -0.7253
405-0.6454 -0.7243
406-0.6454 -0.7238
407-0.6451 -0.723
408-0.6444 -0.7218
409-0.6441 -0.7209
410-0.6442 -0.7207
411-0.6444 -0.7204
412-0.6449 -0.7204
413-0.6454 -0.7205
414-0.646 -0.7207
415-0.647 -0.7214
416-0.6485 -0.7227
417-0.6496 -0.7234
418-0.6507 -0.7241
419-0.652 -0.7252
420-0.6533 -0.7262
421-0.6544 -0.7269
422-0.6557 -0.7279
423-0.6566 -0.7285
424-0.6569 -0.7284
425-0.657 -0.7279
426-0.6571 -0.7277
427-0.6569 -0.727
428-0.6559 -0.7254
429-0.6545 -0.7234
430-0.6531 -0.7214
431-0.6515 -0.7192
432-0.6502 -0.7173
433-0.6489 -0.7155
434-0.6476 -0.7136
435-0.6457 -0.7111
436-0.6441 -0.7089
437-0.6424 -0.7065
438-0.641 -0.7046
439-0.64 -0.703
440-0.6391 -0.7016
441-0.6377 -0.6997
442-0.6369 -0.6984
443-0.6363 -0.6973
444-0.6357 -0.6963
445-0.6349 -0.695
446-0.6341 -0.6937
447-0.6332 -0.6923
448-0.6326 -0.6913
449-0.6318 -0.69
450-0.6314 -0.6891
451-0.6308 -0.6881
452-0.6302 -0.687
453-0.629 -0.6853
454-0.6276 -0.6833
455-0.6261 -0.6813
456-0.6245 -0.6792
457-0.6231 -0.6772
458-0.6217 -0.6754
459-0.6204 -0.6735
460-0.6193 -0.672
461-0.6182 -0.6704
462-0.6173 -0.6691
463-0.6164 -0.6677
464-0.6148 -0.6656
465-0.6129 -0.6632
466-0.611 -0.6608
467-0.6092 -0.6584
468-0.6075 -0.6562
469-0.6058 -0.654
470-0.6035 -0.6512
471-0.6019 -0.649
472-0.6 -0.6467
473-0.5977 -0.6438
474-0.5956 -0.6412
475-0.5929 -0.6379
476-0.59 -0.6345
477-0.5864 -0.6302
478-0.5825 -0.6257
479-0.579 -0.6215
480-0.5753 -0.6173
481-0.5715 -0.6129
482-0.5677 -0.6085
483-0.5639 -0.6041
484-0.5602 -0.5997
485-0.5567 -0.5956
486-0.5524 -0.5907
487-0.548 -0.5857
488-0.5439 -0.581
489-0.5402 -0.5767
490-0.5367 -0.5727
491-0.5339 -0.5694
492-0.5313 -0.5663
493-0.5285 -0.5631
494-0.5256 -0.5597
495-0.5229 -0.5565
496-0.5209 -0.5541
497-0.5196 -0.5525
498-0.5188 -0.5513
499-0.5182 -0.5503
500-0.5175 -0.5493

More formally, we use Monte Carlo simulations to generate $ 10,000$ GARCH(1,1) processes6 for $ X_{t}$, of the size $ n=1000$, and then apply the homoscedastic and heteroscedastic random walk tests to the data. The results for several arbitrary lags, $ q$, are presented in Table 2.3.1.

Table 2.3.1:  Percent of GARCH(1,1) Process Rejected

Confidence Level (φ) q=2 q=4 q=8 q=16 q=32 q=64
φ=95%, Homoscedastic 12.41 12.35 11.57 11.08 9.85 8.12
φ=95%, Heteroscedastic 5.04 5.28 5.30 4.71 4.88 4.88
φ=98%, Homoscedastic 4.39 4.63 4.42 4.12 3.38 3.53
φ=99%, Heteroscedastic 0.83 1.07 1.35 1.41 1.58 2.03

The above table clearly shows that the homoscedastic test is biased towards rejection in the presence of time-varying volatility. This evidence supports our use of the heteroscedasticity-consistent test because it is the forecastability of price changes that is of primary interest in random walk analysis.


3.  Long Memory

Because a new type of test is needed for long memory analysis, we surveyed the literature for alternatives. Although powerful for theoretical modeling and volatility analysis, studies based upon the absolute value of returns (i.e. Ding, Granger, and Engle 1993; and Dacorogna et. al 1993) provide no intuition regarding the direction of a long memory cycle, only its existence. The rescaled range class of test statistics, however, are able to distinguish between positive strong dependence (persistence) and negative strong dependence (mean reversion).

3.1  Methodology

Again we denote $ P_{t}$ as the index level at time $ t$ and define the continuously compounded single period return from $ t-1$ to $ t$ as $ X_{t} \equiv$ ln$ P_{t}-$ln$ P_{t-1}$. To avoid confusion with the notation from our random walk test in section 2, we denote the truncation lag, in days, as $ \xi $. Our long memory methodology follows exactly from Lo (1991).

3.1.1  Classical Hurst-Mandelbrot Rescaled Range

The classical Hurst-Mandelbrot rescaled range statistic is

$\displaystyle \tilde{Q}_{n}\equiv\frac{1}{s_{n}}\left[ \underset{1\leq k\leq n}{\text{Max} }\overset{k}{\underset{j=1}{\sum}}(X_{j}-\bar{X}_{n})-\underset{1\leq k\leq n}{\text{Min}}\underset{j=1}{\overset{k}{\sum}}(X_{j}-\bar{X}_{n})\right] \text{,}$ (9)

where $ s_{n}$ is the usual maximum likelihood standard deviation estimator

$\displaystyle s_{n}\equiv\left[ \frac{1}{n}\underset{j=1}{\overset{n}{\sum}}(X_{j}-\bar {X}_{n})^{2}\right] ^{1/2}$ . (10)

When properly normalized, this statistic weakly converges to the range of the Brownian bridge.

$\displaystyle \tilde{V}_{n}\Longleftarrow\frac{1}{\sqrt{n}}\tilde{Q}_{n}$ . (11)

The classical rescaled range statistic, however, does not distinguish between short- and long-term dependence. Lo (1991) shows that for short-term autocorrelation coefficients, $ \hat{\rho}$, of 50 percent, the mean of $ \tilde{V}_{n}$ may be biased upward by 73 percent, causing a rejection of the null hypothesis at any conventional significance level. Given this weakness and the short-term autoregressive properties of our data described in section 2.2, we selected the modified rescaled range statistic (Lo, 1991) for our long memory analysis because of its invariance to short-term serial correlation.

3.1.2  Lo's Modified Rescaled Range

The modified rescaled range statistic differs only in its denominator to achieve invariance to short memory processes:

$\displaystyle Q_{n\text{ }}\equiv\frac{1}{\hat{\sigma}_{n}(\xi)}\left[ \underset{1\leq k\leq n}{\text{Max}}\overset{k}{\underset{j=1}{\sum}}(X_{j}-\bar{X} _{n})-\underset{1\leq k\leq n}{\text{Min}}\underset{j=1}{\overset{k}{\sum} }(X_{j}-\bar{X}_{n})\right]$ (12)

where

$\displaystyle \hat{\sigma}_{n}^{2}(\xi)\equiv\frac{1}{n}\overset{n}{\underset{j=1}{ {\textstyle\sum} }}(X_{j}-\bar{X}_{n})^{2}+\frac{2}{n}\overset{\xi}{\underset{j=1}{\sum}} \omega_{j}(\xi)\left[ \overset{n}{\underset{i=j+1}{\sum}}(X_{i}-\bar{X} _{n})(X_{i-j}-\bar{X}_{n})\right]$ (13)
$ \ \ $
$\displaystyle \ \ \ \ =\hat{\sigma}_{x}^{2}+2\underset{j=1}{\overset{\xi}{\sum}}\omega _{j}(\xi)\hat{\gamma}_{j},\qquad\omega_{j}(\xi)\equiv1-\frac{j}{\xi+1} ,\qquad\xi<n,$ (14)

and $ \hat{\sigma}_{x}^{2}$ and $ \hat{\gamma}_{j}$ are the sample variance and autocovariance up to lag $ \xi$ of $ X$, respectively. Note that the modified rescaled range simplifies to the classical Hurst-Mandelbrot rescaled range statistic in the special case where $ \xi=0$.

A main criticism of the modified R/S is that there is little guidance about how to select an optimal truncation lag, $ \xi$. If $ \xi$ is chosen too small, significant autocovariances may be ignored, thus biasing the $ Q_{n\text{ }} $statistic. Also, if $ \xi$ is too large relative to the sample size, Lo and MacKinlay (1989) show that the finite-sample distribution deviates significantly from its asymptotic limit.

Andrews (1991) provides an asymptotic data-dependent $ \xi^{\ast}$

$\displaystyle \xi^{\ast}=\left[ k_{n}\right]$   ,  $\displaystyle k_{n}\equiv\left( \frac {3n}{2}\right) ^{\frac{1}{3}}\cdot\left( \frac{2\hat{\rho}}{1-\hat{\rho} ^{2}}\right) ^{\frac{2}{3}}$ , (15)

where $ \left[ k_{n}\right] $ is the greatest integer less than or equal to $ k_{n}$, and $ \hat{\rho}$ is the first-order autocorrelation coefficient. We show the Andrews (1991) data dependent $ \xi^{\ast}$ in section 3.2 below; a broader range of $ \xi$'s are graphed in Appendix 4. Although we report the Andrews $ \xi^{\ast}$ in this paper, it has not been proven to be an optimal method for selecting $ \xi$, and no known method currently exists.

In determining the significance of our results, it can be shown that the modified rescaled range statistic converges to the range of the Brownian bridge

$\displaystyle \frac{1}{\sqrt{n}}Q_{n}\Longrightarrow V_{n}(\xi)$ . (16)

Following from Theorem 3.1 of Lo (1991), the cumulative distribution function (CDF) for the range of the Brownian bridge is given as

$\displaystyle F_{V}(\upsilon)=1+2\overset{\infty}{\underset{k=1}{\sum}}(1-4k^{2}\upsilon ^{2})e^{-2(k\upsilon)^{2}}$ . (17)

Critical values of the two-tailed test can be obtained from the above equation; the most commonly used values are shown in Table 3.1.2.1.

Table 3.1.2.1  Critical Values of the Distribution F(v)

P(V<v) 0.005 0.025 0.050 0.500 0.950 0.975 0.995
v 0.721 0.809 0.861 1.223 1.747 1.862 2.098

Figure 3.1.2.1:  Cumulative Distribution Function of the Modified R/S

Data for Figure 3.1.2.1 immediately follows

Data for Figure 3.1.2.1

vF(v)
0.005 0.000
0.01 0.000
0.015 0.000
0.02 0.000
0.025 0.000
0.03 0.000
0.035 0.000
0.04 0.000
0.045 0.000
0.05 0.000
0.055 0.000
0.06 0.000
0.065 0.000
0.07 0.000
0.075 0.000
0.08 0.000
0.085 0.000
0.09 0.000
0.095 0.000
0.1 0.000
0.105 0.000
0.11 0.000
0.115 0.000
0.12 0.000
0.125 0.000
0.13 0.000
0.135 0.000
0.14 0.000
0.145 0.000
0.15 0.000
0.155 0.000
0.16 0.000
0.165 0.000
0.17 0.000
0.175 0.000
0.18 0.000
0.185 0.000
0.19 0.000
0.195 0.000
0.2 0.000
0.205 0.000
0.21 0.000
0.215 0.000
0.22 0.000
0.225 0.000
0.23 0.000
0.235 0.000
0.24 0.000
0.245 0.000
0.25 0.000
0.255 0.000
0.26 0.000
0.265 0.000
0.27 0.000
0.275 0.000
0.28 0.000
0.285 0.000
0.29 0.000
0.295 0.000
0.3 0.000
0.305 0.000
0.31 0.000
0.315 0.000
0.32 0.000
0.325 0.000
0.33 0.000
0.335 0.000
0.34 0.000
0.345 0.000
0.35 0.000
0.355 0.000
0.36 0.000
0.365 0.000
0.37 0.000
0.375 0.000
0.38 0.000
0.385 0.000
0.39 0.000
0.395 0.000
0.4 0.000
0.405 0.000
0.41 0.000
0.415 0.000
0.42 0.000
0.425 0.000
0.43 0.000
0.435 0.000
0.44 0.000
0.445 0.000
0.45 0.000
0.455 0.000
0.46 0.000
0.465 0.000
0.47 0.000
0.475 0.000
0.48 0.000
0.485 0.000
0.49 0.000
0.495 0.000
0.5 0.000
0.505 0.000
0.51 0.000
0.515 0.000
0.52 0.000
0.525 0.000
0.53 0.000
0.535 0.000
0.54 0.000
0.545 0.000
0.55 0.000
0.555 0.000
0.56 0.000
0.565 0.000
0.57 0.000
0.575 0.000
0.58 0.000
0.585 0.000
0.59 0.000
0.595 0.000
0.6 0.000
0.605 0.000
0.61 0.000
0.615 0.000
0.62 0.000
0.625 0.000
0.63 0.000
0.635 0.001
0.64 0.001
0.645 0.001
0.65 0.001
0.655 0.001
0.66 0.001
0.665 0.001
0.67 0.001
0.675 0.002
0.68 0.002
0.685 0.002
0.69 0.002
0.695 0.003
0.7 0.003
0.705 0.003
0.71 0.004
0.715 0.004
0.72 0.005
0.725 0.005
0.73 0.006
0.735 0.007
0.74 0.007
0.745 0.008
0.75 0.009
0.755 0.010
0.76 0.011
0.765 0.012
0.77 0.013
0.775 0.014
0.78 0.016
0.785 0.017
0.79 0.019
0.795 0.020
0.8 0.022
0.805 0.023
0.81 0.025
0.815 0.027
0.82 0.029
0.825 0.031
0.83 0.034
0.835 0.036
0.84 0.038
0.845 0.041
0.85 0.044
0.855 0.046
0.86 0.049
0.865 0.052
0.87 0.055
0.875 0.059
0.88 0.062
0.885 0.066
0.89 0.069
0.895 0.073
0.9 0.077
0.905 0.081
0.91 0.085
0.915 0.089
0.92 0.093
0.925 0.098
0.93 0.102
0.935 0.107
0.94 0.112
0.945 0.117
0.95 0.122
0.955 0.127
0.96 0.132
0.965 0.138
0.97 0.143
0.975 0.149
0.98 0.154
0.985 0.160
0.99 0.166
0.995 0.172
1 0.178
1.005 0.184
1.01 0.190
1.015 0.197
1.02 0.203
1.025 0.210
1.03 0.216
1.035 0.223
1.04 0.230
1.045 0.236
1.05 0.243
1.055 0.250
1.06 0.257
1.065 0.264
1.07 0.271
1.075 0.278
1.08 0.286
1.085 0.293
1.09 0.300
1.095 0.307
1.1 0.315
1.105 0.322
1.11 0.330
1.115 0.337
1.12 0.345
1.125 0.352
1.13 0.360
1.135 0.367
1.14 0.375
1.145 0.382
1.15 0.390
1.155 0.397
1.16 0.405
1.165 0.412
1.17 0.420
1.175 0.428
1.18 0.435
1.185 0.443
1.19 0.450
1.195 0.458
1.2 0.465
1.205 0.473
1.21 0.480
1.215 0.488
1.22 0.495
1.225 0.502
1.23 0.510
1.235 0.517
1.24 0.524
1.245 0.531
1.25 0.539
1.255 0.546
1.26 0.553
1.265 0.560
1.27 0.567
1.275 0.574
1.28 0.581
1.285 0.588
1.29 0.594
1.295 0.601
1.3 0.608
1.305 0.614
1.31 0.621
1.315 0.627
1.32 0.634
1.325 0.640
1.33 0.647
1.335 0.653
1.34 0.659
1.345 0.665
1.35 0.671
1.355 0.677
1.36 0.683
1.365 0.689
1.37 0.695
1.375 0.701
1.38 0.707
1.385 0.712
1.39 0.718
1.395 0.723
1.4 0.729
1.405 0.734
1.41 0.739
1.415 0.744
1.42 0.750
1.425 0.755
1.43 0.760
1.435 0.765
1.44 0.769
1.445 0.774
1.45 0.779
1.455 0.784
1.46 0.788
1.465 0.793
1.47 0.797
1.475 0.801
1.48 0.806
1.485 0.810
1.49 0.814
1.495 0.818
1.5 0.822
1.505 0.826
1.51 0.830
1.515 0.834
1.52 0.838
1.525 0.841
1.53 0.845
1.535 0.849
1.54 0.852
1.545 0.856
1.55 0.859
1.555 0.862
1.56 0.866
1.565 0.869
1.57 0.872
1.575 0.875
1.58 0.878
1.585 0.881
1.59 0.884
1.595 0.887
1.6 0.890
1.605 0.892
1.61 0.895
1.615 0.898
1.62 0.900
1.625 0.903
1.63 0.905
1.635 0.908
1.64 0.910
1.645 0.912
1.65 0.915
1.655 0.917
1.66 0.919
1.665 0.921
1.67 0.923
1.675 0.925
1.68 0.927
1.685 0.929
1.69 0.931
1.695 0.933
1.7 0.935
1.705 0.937
1.71 0.938
1.715 0.940
1.72 0.942
1.725 0.943
1.73 0.945
1.735 0.946
1.74 0.948
1.745 0.949
1.75 0.951
1.755 0.952
1.76 0.954
1.765 0.955
1.77 0.956
1.775 0.957
1.78 0.959
1.785 0.960
1.79 0.961
1.795 0.962
1.8 0.963
1.805 0.964
1.81 0.966
1.815 0.967
1.82 0.968
1.825 0.969
1.83 0.969
1.835 0.970
1.84 0.971
1.845 0.972
1.85 0.973
1.855 0.974
1.86 0.975
1.865 0.975
1.87 0.976
1.875 0.977
1.88 0.978
1.885 0.978
1.89 0.979
1.895 0.980
1.9 0.980
1.905 0.981
1.91 0.982
1.915 0.982
1.92 0.983
1.925 0.983
1.93 0.984
1.935 0.984
1.94 0.985
1.945 0.985
1.95 0.986
1.955 0.986
1.96 0.987
1.965 0.987
1.97 0.988
1.975 0.988
1.98 0.988
1.985 0.989
1.99 0.989
1.995 0.990
2 0.990
2.005 0.990
2.01 0.991
2.015 0.991
2.02 0.991
2.025 0.992
2.03 0.992
2.035 0.992
2.04 0.992
2.045 0.993
2.05 0.993
2.055 0.993
2.06 0.993
2.065 0.994
2.07 0.994
2.075 0.994
2.08 0.994
2.085 0.995
2.09 0.995
2.095 0.995
2.1 0.995
2.105 0.995
2.11 0.995
2.115 0.996
2.12 0.996
2.125 0.996
2.13 0.996
2.135 0.996
2.14 0.996
2.145 0.997
2.15 0.997
2.155 0.997
2.16 0.997
2.165 0.997
2.17 0.997
2.175 0.997
2.18 0.997
2.185 0.997
2.19 0.998
2.195 0.998
2.2 0.998
2.205 0.998
2.21 0.998
2.215 0.998
2.22 0.998
2.225 0.998
2.23 0.998
2.235 0.998
2.24 0.998
2.245 0.998
2.25 0.999
2.255 0.999
2.26 0.999
2.265 0.999
2.27 0.999
2.275 0.999
2.28 0.999
2.285 0.999
2.29 0.999
2.295 0.999
2.3 0.999
2.305 0.999
2.31 0.999
2.315 0.999
2.32 0.999
2.325 0.999
2.33 0.999
2.335 0.999
2.34 0.999
2.345 0.999
2.35 0.999
2.355 0.999
2.36 0.999
2.365 0.999
2.37 0.999
2.375 1.000
2.38 1.000
2.385 1.000
2.39 1.000
2.395 1.000
2.4 1.000
2.405 1.000
2.41 1.000
2.415 1.000
2.42 1.000
2.425 1.000
2.43 1.000
2.435 1.000
2.44 1.000
2.445 1.000
2.45 1.000
2.455 1.000
2.46 1.000
2.465 1.000
2.47 1.000
2.475 1.000
2.48 1.000
2.485 1.000
2.49 1.000
2.495 1.000
2.5 1.000
2.505 1.000
2.51 1.000
2.515 1.000
2.52 1.000
2.525 1.000
2.53 1.000
2.535 1.000
2.54 1.000
2.545 1.000
2.55 1.000
2.555 1.000
2.56 1.000
2.565 1.000
2.57 1.000
2.575 1.000
2.58 1.000
2.585 1.000
2.59 1.000
2.595 1.000
2.6 1.000
2.605 1.000
2.61 1.000
2.615 1.000
2.62 1.000
2.625 1.000
2.63 1.000
2.635 1.000
2.64 1.000
2.645 1.000
2.65 1.000
2.655 1.000
2.66 1.000
2.665 1.000
2.67 1.000
2.675 1.000
2.68 1.000
2.685 1.000
2.69 1.000
2.695 1.000
2.7 1.000
2.705 1.000
2.71 1.000
2.715 1.000
2.72 1.000
2.725 1.000
2.73 1.000
2.735 1.000
2.74 1.000
2.745 1.000
2.75 1.000
2.755 1.000
2.76 1.000
2.765 1.000
2.77 1.000
2.775 1.000
2.78 1.000
2.785 1.000
2.79 1.000
2.795 1.000
2.8 1.000
2.805 1.000
2.81 1.000
2.815 1.000
2.82 1.000
2.825 1.000
2.83 1.000
2.835 1.000
2.84 1.000
2.845 1.000
2.85 1.000
2.855 1.000
2.86 1.000
2.865 1.000
2.87 1.000
2.875 1.000
2.88 1.000
2.885 1.000
2.89 1.000
2.895 1.000
2.9 1.000
2.905 1.000
2.91 1.000
2.915 1.000
2.92 1.000
2.925 1.000
2.93 1.000
2.935 1.000
2.94 1.000
2.945 1.000
2.95 1.000
2.955 1.000
2.96 1.000
2.965 1.000
2.97 1.000
2.975 1.000
2.98 1.000
2.985 1.000
2.99 1.000
2.995 1.000
3 1.000

3.2  Results

The results of our long memory analysis are shown in detail in Appendix 4. Again, the dashed orange and red lines represent 95 and 99 percent rejection levels of the modified rescaled range hypothesis test, respectively. Significantly large $ V$-values indicate positive strong dependence. $ V$-values below the lower rejection band show negative strong dependence. Table 3.2.1 reports numerical results of our modified rescaled analysis using Andrews' (1991) data-dependent $ \xi^{\ast}.$7

We find little evidence for long-term memory in global equity indices. With adjustments for short-term autocorrelations of up to 250 trading days, approximately one year, the null hypothesis of no long term dependence cannot be rejected8 for 36 of the 44 equity markets studied. Criticisms levied against the modified rescaled range by Baillie (1996), for example, cite that

...a major practical difficulty concerns the choice of $ q[\xi]$ and how to distinguish between short range dependencies and long range dependencies.

Our graphical results in Appendix 4 do not support this claim. We fail to reject the null hypothesis at every integer lag for the United States, United Kingdom and many other emerging and industrialized equity markets. Furthermore, our findings are largely consistent with other analyses of the U.S. (Lo, 1991) and global (Chow et. al, 1996) equity markets.

In the foreign exchange markets, we find great disparity in the long memory evidence between emerging and industrialized economies. Contrary to Mulligan (2000),9 we find no evidence of long memory in the bilateral trade of U.S. dollars with other advanced market currencies. A likely reason for this disparity is Mulligan's use of monthly averages instead of point data, which may bias results in the presence of short-term dependece in the daily data. We reject the null hypothesis for many emerging economies, however, particularly in Latin America.

We find very little evidence of long memory in most commodity markets. However, Corrazza et. al. (1997) found fractal returns in the futures markets for soybeans, wheat, oats, and corn. We similarly found long memory in the spot returns of the soybeans market.

Table 3.2.1a. Results of the Modified R/S Test for Optimal Lag ξ - By Country

Country Equity Indicies: ξ* Equity Indicies: V(ξ*) Foreign Exchange : ξ* Foreign Exchange: V(ξ*)

Argentina

4

1.50

2

 1.91*

Brazil

5

1.31

3

 1.89*

Chile

14

1.75

3

 1.88*

Colombia

7

1.62

0

 1.91*

Mexico

7

1.38

0

1.00

Peru

11

 2.31**

2

1.41

Venezuela

8

1.25

 

 

China

2

1.38

 

 

Hong Kong

4

1.37

 

 

Indonesia

12

1.66

6

1.46

India

6

1.45

9

 2.12**

South Korea

6

 1.88*

7

 1.95*

Malaysia

8

1.50

1

1.35

Philippines

9

1.37

5

1.67

Russia

7

1.66

8

 2.00*

Singapore

9

1.48

5

1.34

Taiwan

5

1.50

 

 

Thailand

7

1.79

4

1.57

Israel

1

0.98

2

 2.05*

Kuwait

1

1.85

 

 

Nigeria

15

1.21

12

1.23

Saudi Arabia

2

2.20**

 

 

South Africa

4

1.43

1

 2.01*

Turkey

4

1.47

5

1.36

UAE

2

 2.16**

 

 

Australia

7

1.36

3

1.30

Belgium

8

1.85

 

 

Canada

9

0.99

2

1.64

Czech Republic

5

1.86

1

1.71

Denmark

3

 2.02*

 

 

European Union

 

 

0

1.51

France

2

1.54

 

 

Germany

1

1.58

 

 

Hungary

5

1.39

 

 

Italy

11

1.61

 

 

Japan

7

 1.95*

3

1.23

Netherlands

0

1.40

 

 

Norway

1

 2.12**

0

1.43

New Zealand

5

1.00

2

1.45

Poland

6

1.32

3

1.79

Sweden

1

 1.93*

0

1.48

Spain

2

1.63

 

 

Switzerland

2

1.48

2

1.38

UK

2

1.18

4

1.44

US

5

1.57

 

 

* and ** denote significane at the 95 and 99 percent confidence levels, respectively


Table 3.2.1b. Results of the Modified R/S Test for Optimal Lag ξ - By Commodity

Commodity
ξ*
V(ξ*)

Crude Oil

0

0.95

Gasoline

1

1.06

Natural Gas

0

0.92

Heating Oil

3

1.02

Copper

4

1.28

Aluminum

2

1.26

Lead

4

1.26

Nickel

1

1.30

Tin

4

1.54

Zinc

0

1.47

Gold

3

1.03

Platinum

2

1.39

Silver

2

1.00

Cotton

2

1.58

Rubber

13

1.21

Corn

0

1.65

Wheat

5

1.19

Soybeans

1

 2.08*

Cattle

2

 0.72**

Cocoa

2

0.90

Coffee

0

1.25

Sugar

4

1.57

* and ** denote significane at the 95 and 99 percent confidence levels, respectively


4.  Conclusion

This paper presents an extensive analysis of short- and long-term memory in the returns of international financial data. The random walk section attempts to answer the question, can asset prices be forecasted based on historical price information alone? Using a heteroscedasticity-consistent test, we conclude that financial data are broadly unpredictable with a few notable exceptions. First, energy prices exhibit mean-reverting price behavior. Second, markets with poorer risk-adjusted performance are more likely the reject the random walk. We expect that prolonged, weak performance in these markets has deterred analyst coverage, resulting in relatively low informational efficiency. This idea is consistent with contrarian investment strategies which seek to earn positive abnormal returns in depressed markets.

Much of the empirical literature on long memory concerns the rate of decay in the autocorrelation of volatility. Although important for applications in risk management, options and other derivative markets, long memory in volatility does not provide intuition regarding the direction of the cycle in returns. When Hurst (1951) set out to identify long memory patterns in the Nile River, for example, he was not concerned with identifying volatility in sediment discharge, but the prediction of flood (positive) and drought (negative) cycles to improve river management in the delta. We are concerned with similar questions in asset pricing. Can we identify long term cycles in asset prices to earn excess returns? We attempt to answer this question via a modernization of Hurst's test, the modified rescaled range statistic, and, in financial asset returns, we find very little evidence of long memory cycles. The most promising area for further long memory research appears to be the bilateral exchange of U.S. dollars with the currencies of Latin American economies.


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Appendix 1. Data

Appendix 1.1 Equity Indices

Daily equity index data for each country were downloaded from Bloomberg. We downloaded the fields "px_last" (last price) and "eqy_last_dps_gross" (dividends per share) to create a total return series according to the fundamental relationship:

$\displaystyle P_{1}=\alpha_{1\text{,}}$ (18)

$\displaystyle P_{t}=P_{t-1}\left[ (\frac{\varphi_{t}}{\alpha_{t-1}})+(\frac{\alpha_{t} }{\alpha_{t-1}})\right]$    . (19)

We initialized the first observation of the total return index, $ P_{1}$, to equal the basic index level, $ \alpha_{1}$. Equation 19 was then used to construct the total return index series as the sum of the dividend and capital gains yields, respectively, where $ \varphi_{t}$ are dividends per share. Because our Bloomberg download program only provided two decimal places, and indices are calculated with an arbitrary base (i.e. 1995=100), time series of countries experiencing extraordinary growth or crises were truncated to avoid rounding errors. For example, at the beginning of the dataset, some countries (like Peru), had index values at or near "0.00". Returns calculated on such low price levels were inherently undefined or extremely volatile, and thus not representative of the historical record. As a rule-of-thumb, we corrected for this by eliminating the first $ t$ observations where $ \alpha_{t}<100$, leaving a residual rounding error no greater than $ \frac{\alpha_{t}}{20000}$.

Appendix Table 1.1

CountryTickerDescriptionSample (mm/dd/yy)
Latin America: (AR) ArgentinaMARMerval Index01/03/00 - 03/07/08
Latin America: (BZ) BrazilIBXIBX Index01/02/99 - 03/07/08
Latin America: (CL) ChileIGPAIPSA Stock Index01/03/90 - 03/07/08
Latin America: (CO) ColombiaIGBCIGBC Stock Index07/04/01 - 03/07/08
Latin America: (MX) MexicoMEXBOLBolsa Stock Index01/03/89 - 03/07/08
Latin America: (PE) PeruIGBVLPeru Lima General Index01/03/92 - 03/07/08
Latin America: (VE) VenezuelaIBVCIBC Stock Index01/03/94 - 03/07/08
Emerging Asia: (CH) ChinaSHCOMPShanghai Composite Index01/04/95 - 03/07/08
Emerging Asia: (HK) Hong KongHSIHang Seng Stock Index11/25/69 - 03/07/08
Emerging Asia: (ID) IndonesiaJCIJakarta Stock Index04/05/83 - 03/07/08
Emerging Asia: (IN) IndiaSENSEXSensex Stock Index04/04/79 - 03/07/08
Emerging Asia: (KO) South KoreaKOSPIKOSPI Stock Index01/05/80 - 03/07/08
Emerging Asia: (MA) MalaysiaKLCIKuala Lumpur Composite01/04/77 - 03/07/08
Emerging Asia: (PH) PhilippinesPCOMPPSEI Stock Index01/05/87 - 03/07/08
Emerging Asia: (RU) RussiaRTSI$Russian Trading System09/04/95 - 03/07/08
Emerging Asia: (SI) SingaporeSESALLAll-Equities Stock Index01/03/75 - 03/07/08
Emerging Asia: (TA) TaiwanTWSETWSE Stock Index01/05/73 - 03/07/08
Emerging Asia: (TH) ThailandSETBangkok SET Stock Index07/03/87 - 03/07/08
Middle East and Africa: (IS) IsraelTA-25Tel Aviv 25 Stock Index01/05/92 - 03/07/08
Middle East and Africa: (KW) KuwaitKWSEIDXKuwait SE Unweighed Index06/18/01 - 03/07/08
Middle East and Africa: (NG) NigeriaNGSEINDXNigeria Stock Exchange01/05/98 - 03/07/08
Middle East and Africa: (SA) Saudi ArabiaSASEIDXTadawul All-Shares01/29/94 - 03/07/08
Middle East and Africa: (SF) South AfricaJALSHJSE All-Shares Stock Index07/03/95 - 03/07/08
Middle East and Africa: (TK) TurkeyXU100Istanbul National 100 Index01/03/90 - 03/07/08
Middle East and Africa: (UA) UAEDFMGIDubai General Stock Index01/03/04 - 03/07/08
Industrialized Economies: (AL) AustraliaAS30All Ordinaries Stock Index01/02/80 - 03/07/08
Industrialized Economies: (BE) BelgiumBELSTKBelgian All-Shares10/04/88 - 03/07/08
Industrialized Economies: (CA) CanadaSPTSXS&P Toronto Stock Index01/04/77 - 03/07/08
Industrialized Economies: (CZ) Czech RepublicPXPX Stock Index09/20/94 - 03/07/08
Industrialized Economies: (DN) DenmarkKAXOMX Copenhagen01/02/96 - 03/07/08
Industrialized Economies: (FR) FranceSBF250SBF 250 Stock Index01/02/91 - 03/07/08
Industrialized Economies: (GE) GermanyHDAXHDAX Stock Index01/04/88 - 03/07/08
Industrialized Economies: (HU) HungaryBUXBudapest Stock Exchange01/03/91 - 03/07/08
Industrialized Economies: (IT) ItalyITSMBANCBacchi Stock Index01/03/73 - 03/07/08
Industrialized Economies: (JA) JapanTPXTOPIX Stock Index01/06/70 - 03/07/08
Industrialized Economies: (NE) NetherlandsAEXAmsterdam Exchanges Index01/04/83 - 03/07/08
Industrialized Economies: (NO) NorwayOSEAXOslo All-Shares Stock Index01/02/96 - 03/07/08
Industrialized Economies: (NZ) New ZealandNZSEAll Ordinaries Stock Index03/31/92 - 03/07/08
Industrialized Economies: (PL) PolandWIGWSE WIG Index04/23/91 - 03/07/08
Industrialized Economies: (SD) SwedenSWSMAFFRAffarsvarlden Stock Index01/04/00 - 03/07/08
Industrialized Economies: (SP) SpainMADXMadrid Stock Index02/19/93 - 03/07/08
Industrialized Economies: (SZ) SwitzerlandSMISwiss Market Stock Index07/04/88 - 03/07/08
Industrialized Economies: (UK) United KingdomASXFTSE All-Shares Stock Index01/03/85 - 03/07/08
Industrialized Economies: (US) United StatesSPXS&P 500 Index01/05/70 - 03/07/08

Appendix 1.2 Commodities

The commodity data are daily closing prices in the spot market. Rubber price data is from Bloomberg, and all other commodities are from the Commodity Research Bureau, Final Markets database.

Appendix Table 1.2

CommoditySource10DescriptionSample (mm/dd/yy)
Energy: Crude OilNYMEXWest Texas Intermediate crude oil, Cushing OK01/02/85 - 03/07/08
Energy: Natural GasNYMEXNatural gas, Henry Hub10/29/93 - 03/07/08
Energy: Heating OilNYMEXHeating oil #2, fuel oil09/02/03 - 03/07/08
Energy: GasolineNYMEXGasoline, unleaded, regular non-oxygenated09/02/03 - 03/07/08
Metals: AluminumLMEAluminum, high grade09/01/03 - 03/07/08
Metals: CopperNYMEX/COMEXCopper high grade, scrap #2 wire09/02/03 - 03/07/08
Metals: GoldNYMEX/COMEXGold09/01/03 - 03/07/08
Metals: LeadUSGSLead pig09/02/03 - 03/07/08
Metals: NickelLMENickel09/01/03 - 03/07/08
Metals: PlatinumNYMEX/COMEXPlatinum09/02/03 - 03/07/08
Metals: SilverNYMEX/COMEXSilver09/01/03 - 03/07/08
Metals: TinUSGSTin straights, composite09/02/03 - 03/07/08
Metals: ZincAMMZinc, prime western, domestic09/02/03 - 03/07/08
Agriculture: CattleCMELive cattle, choice average, Texas/Oklahoma09/02/03 - 03/07/08
Agriculture: CocoaNYBOTCocoa, Ivory Coast09/02/03 - 03/07/08
Agriculture: CoffeeUSDACoffee, Brazilian09/02/03 - 03/07/08
Agriculture: CornCBOTCorn, #2 yellow10/25/01 - 03/07/08
Agriculture: CottonUSDACotton, 1-1/1609/02/03 - 03/07/08
Agriculture: RubberMARBStandard Rubber #2007/20/01 - 03/07/08
Agriculture: SoybeanCBOTSoybeans, #1 yellow09/02/03 - 03/07/08
Agriculture: SugarNYBOTSugar #11, world raw09/02/03 - 03/07/08
Agriculture: WheatKCBOTWheat, #2 hard winter09/02/03 - 03/07/08

Appendix 1.3 Foreign Exchange Rates

Nominal bilateral exchange rates are in units of foreign currency per U.S. dollar. The data for Australia, Brazil, Canada, Denmark, the European Monetary Union, India, Japan, Malaysia, Mexico, New Zealand, Norway, Singapore, South Africa, South Korea, Sweden, Switzerland, Taiwan, Thailand and the United Kingdom are the 12 PM rates from the Federal Reserve Bank of New York.11 All other exchange rate data are closing prices from Bloomberg. Countries currently employing a fixed or pegged exchange rate regime are ignored in this study because calculations of temporal dependence are meaningless under fixed prices. Currency classifications are as defined in the 2006 IMF Annual Report on Exchange Arrangements and Exchange Restrictions.

Appendix Table 1.3

CountryCurrencyClassificationSample (mm/dd/yy)
Latin America: (AR) ArgentinaPesoManaged Float02/11/02 - 03/07/08
Latin America: (BZ) BrazilRealIndependent Float01/15/99 - 03/07/08
Latin America: (CL) ChilePesoIndependent Float09/03/99 - 03/07/08
Latin America: (CO) ColombiaPesoManaged Float09/26/99 - 03/07/08
Latin America: (MX) MexicoPesoIndependent Float08/02/96 - 03/07/08
Latin America: (PE) PeruNuevo SolManaged Float09/01/97 - 03/07/08
Emerging Asia: (ID) Indonesia RupiahManaged Float08/15/97 - 03/07/08
Emerging Asia: (IN) IndiaRupeeManaged Float01/02/73 - 03/07/08
Emerging Asia: (KO) South KoreaWonIndependent Float04/13/81 - 03/07/08
Emerging Asia: (MA) MalaysiaRinggitManaged Float01/22/05 - 03/07/08
Emerging Asia: (PH) PhilippinesPesoIndependent Float03/16/98 - 03/07/08
Emerging Asia: (RU) RussiaRubleManaged Float01/06/99 - 03/07/08
Emerging Asia: (SI) SingaporeDollarManaged Float01/02/81 - 03/07/08
Emerging Asia: (TH) ThailandBahtManaged Float07/09/97 - 03/07/08
Middle East and Africa: (IS) IsraelSheqelIndependent Float12/18/91 - 03/07/08
Middle East and Africa: (NG) NigeriaNairaManaged Float01/04/99 - 03/07/08
Middle East and Africa: (SF) South AfricaRandIndependent Float01/06/71 - 03/07/08
Middle East and Africa: (TK) TurkeyNew LiraIndependent Float02/28/01 - 03/07/08
Industrialized Economies: (AL) AustraliaDollarIndependent Float01/02/75 - 03/07/08
Industrialized Economies: (CA) CanadaDollarIndependent Float01/04/71 - 03/07/08
Industrialized Economies: (CZ) Czech RepublicKorunaManaged Float01/16/96 - 03/07/08
Industrialized Economies: (EU) European Union12EuroIndependent Float01/04/99 - 03/07/08
Industrialized Economies: (JA) JapanYenIndependent Float01/04/71 - 03/07/08
Industrialized Economies: (NO) NorwayKroneIndependent Float01/04/71 - 03/07/08
Industrialized Economies: (NZ) New ZealandDollarIndependent Float01/04/71 - 03/07/08
Industrialized Economies: (PL) PolandZlotyIndependent Float04/24/96 - 03/07/08
Industrialized Economies: (SD) SwedenKronaIndependent Float01/04/71 - 03/07/08
Industrialized Economies: (SZ) SwitzerlandFrancIndependent Float01/04/71 - 03/07/08
Industrialized Economies: (UK) United KingdomPoundIndependent Float01/04/71 - 03/07/08

Appendix 2.  Summary Statistics

Appendix 2.1.  Equity Indices

Country

Sample Size

Mean

Standard Deviation

Skewness

Excess Kurtosis

Jarque-Bera Statistic

Argentina

1940

0.051

2.18

0.17

5.41

 2377.82**

Brazil

2879

0.120

2.01

0.61

16.31

 32072.80**

Chile

4358

0.069

0.78

0.16

3.82

 2666.04**

Colombia

1528

0.167

1.51

-0.06

14.38

 13165.80**

Mexico

4644

0.106

1.57

-0.09

5.68

 6253.92**

Peru

3866

0.127

1.46

0.22

6.70

 7259.93**

Venezuela

3224

0.133

1.82

-0.13

13.38

 24045.15**

China

3121

0.060

1.84

0.55

21.33

 59297.77**

Hong Kong

9042

0.057

1.85

-0.37

12.39

 58083.83**

Indonesia

5795

0.059

1.57

4.00

97.61

 2316205.03**

India

5639

0.051

1.59

-0.06

4.61

 5005.44**

Korea

6620

0.043

1.62

-0.16

4.59

 5847.42**

Malaysia

7316

0.036

1.40

-0.61

32.44

 321301.57**

Philippines

5079

0.027

1.67

0.10

9.49

 19048.88**

Russia

2995

0.078

2.70

-0.42

6.50

 5357.90**

Singapore

7951

0.036

1.21

-1.32

34.04

 386172.07**

Taiwan

8165

0.046

1.76

-0.23

3.77

 4903.65**

Thailand

4803

0.029

1.70

0.02

6.23

 7773.66**

Israel

2301

0.063

1.74

-0.17

3.70

 1325.61**

Kuwait

736

0.228

1.27

-0.50

5.97

 1122.54**

Nigeria

2186

0.081

0.86

-0.98

15.52

 22303.69**

Saudi Arabia

2025

0.063

1.62

-0.94

15.32

 20113.67**

South Africa

3054

0.050

1.20

-0.74

7.86

 8144.32**

Turkey

4403

0.163

2.93

0.02

3.48

 2220.95**

UAE

627

0.252

2.31

0.14

3.94

 408.59**

Australia

6978

0.036

0.95

-4.53

127.01

 4714368.66**

Belgium

4679

0.030

0.89

0.05

7.11

 9847.77**

Canada

7602

0.035

0.85

-0.99

13.53

 59242.83**

Czech Republic

3218

0.014

1.21

-0.22

3.09

 1307.13**

Denmark

2975

0.043

0.94

-0.51

2.55

 933.22**

France

4234

0.030

1.14

-0.21

3.45

 2130.20**

Germany

4965

0.038

1.30

-0.56

6.98

 10339.31**

Hungary

4163

0.074

1.60

-0.79

13.69

 32927.86**

Italy

8545

0.027

1.26

-0.46

5.22

 10001.44**

Japan

9027

0.017

1.04

-0.52

11.62

 51222.52**

Netherlands

6275

0.035

1.28

-0.32

8.22

 17771.00**

Norway

2981

0.037

1.19

-0.53

3.38

 1560.75**

New Zealand

3902

0.041

0.80

0.00

8.70

 12299.44**

Poland

3348

0.053

1.90

-0.17

7.36

 7572.63**

Sweden

1995

-0.004

1.41

-0.11

2.42

 490.24**

Spain

3641

0.045

1.17

-0.36

3.22

 1649.38**

Switzerland

4824

0.029

1.13

-0.52

7.03

 10142.03**

UK

5864

0.033

0.96

-0.81

11.71

 34140.18**

US

9317

0.040

0.99

-1.43

34.83

 474220.14**

* and ** represent significance at the 95 and 99 percent confidence levels, respectively


Appendix 2.2.  Commodities

Commodity

Sample Size

Mean

Standard Deviation

Skewness

Excess Kurtosis

Jarque-Bera Statistic

Crude Oil

5630

0.016

2.45

-1.22

18.93

 85435.26**

Gasoline

1086

0.090

2.96

-0.15

7.08

 2271.70**

Natural Gas

3405

0.080

4.89

0.70

24.74

 87144.91**

Heating Oil

1086

0.114

2.33

0.26

1.06

 63.64**

Copper

1086

0.109

1.99

-0.50

3.10

 480.71**

Aluminum

1114

0.074

1.45

-0.25

2.11

 219.03**

Lead

1087

0.109

2.03

-0.37

5.89

 1597.30**

Nickel

1114

0.117

2.65

-0.35

3.32

 535.69**

Tin

1097

0.111

1.69

-0.40

3.79

 685.51**

Zinc

1097

0.079

2.00

-0.50

2.60

 356.57**

Gold

1166

0.078

1.11

-0.57

2.58

 385.74**

Platinum

1097

0.086

1.25

-0.02

5.48

 1372.32**

Silver

1164

0.104

2.04

-1.41

9.79

 5032.06**

Cotton

1087

0.017

1.73

0.29

11.91

 6433.98**

Rubber

1548

0.088

0.87

-0.28

2.48

 416.12**

Corn

1537

0.059

1.76

0.15

1.23

 103.49**

Wheat

1092

0.088

2.28

-0.49

64.15

 187269.43**

Soybeans

1090

0.057

1.75

-0.82

4.35

 983.71**

Cattle

1108

0.022

1.43

0.24

3.64

 622.91**

Cocoa

1086

0.044

1.73

-0.24

3.39

 530.14**

Coffee

1085

0.084

1.98

0.30

4.31

 857.82**

Sugar

1086

0.071

1.91

-0.13

2.27

 236.46**

* and ** represent significance at the 95 and 99 percent confidence levels, respectively


Appendix 2.3.  Foreign Exchange Rates

Country

Sample Size

Mean

Standard Deviation

Skewness

Excess Kurtosis

Jarque-Bera Statistic

Argentina

1544

0.030

1.15

3.18

102.82

 682741.37**

Brazil

2218

-0.004

1.07

0.54

13.98

 18173.92**

Chile

2175

-0.007

0.54

0.07

2.14

 414.97**

Colombia

2163

-0.003

0.53

0.06

6.49

 3803.08**

Mexico

2808

0.010

0.51

0.87

8.19

 8195.30**

Peru

543

0.049

0.30

-0.01

8.73

 1726.16**

Indonesia

2695

0.036

1.85

1.71

36.17

 148223.94**

India

8477

0.017

0.47

4.71

129.04

 5912848.31**

Korea

6427

0.003

0.58

3.45

158.07

 6704119.60**

Malaysia

638

-0.027

0.25

-0.05

3.24

 279.5911**

Philippines

2561

0.001

0.56

-7.75

218.71

 5130106.64**

Russia

2355

0.002

0.37

1.98

75.65

 563129.97**

Singapore

6571

-0.008

0.33

-0.80

15.94

 70261.65**

Thailand

2587

-0.002

0.73

-0.51

15.62

 26420.83**

Israel

3819

0.010

0.43

1.47

25.24

 102758.53**

Nigeria

2263

0.011

1.47

0.27

16.27

 24986.60**

South Africa

8933

0.028

0.83

1.93

53.89

 1086480.52**

Turkey

1832

0.018

1.24

1.43

23.55

 42949.21**

Australia

8015

0.002

0.62

4.62

128.27

 5523084.78**

Canada

8977

-0.001

0.32

-0.01

3.82

 5445.18**

Czech Republic

3122

-0.016

0.69

0.53

8.09

 8663.15**

European Union

2226

-0.013

0.58

-0.02

0.85

 67.46**

Japan

8963

-0.013

0.62

-0.41

5.94

 13425.10**

Norway

8967

-0.004

0.59

0.36

7.98

 24018.13**

New Zealand

8949

0.002

0.67

2.72

66.20

 1644907.54**

Poland

3049

-0.006

0.64

0.28

2.82

 1049.42**

Sweden

8967

-0.002

0.59

1.02

19.68

 146297.76**

Switzerland

8969

-0.016

0.71

0.01

3.77

 5317.29**

UK

8969

0.001

0.57

0.14

4.20

 6608.25**

* and ** represent significance at the 95 and 99 percent confidence levels, respectively


Appendix 3.  Random Walk Hypothesis Tests

For all figures in Appendix 3, the 95% critical values are plus-or-minus 1.96, and the 99% critical values are plus-or-minus 2.58. The critical values do not depend upon q.

Data for figure immediately follows

Data for Appendix 3 - Random Walk Hypothesis Tests: Equity (Russia - South Korea)

qArgentinaBrazilChileColombiaMexicoPeruVenezuelaChinaHong KongIndonesiaIndiaSouth Korea
22.807 -0.636 4.594 0.646 1.146 1.037 1.787 0.346 2.983 -0.260 -0.482 -0.218
32.761 0.361 5.598 0.938 1.127 2.411 1.843 0.440 3.942 -0.006 0.410 0.043
42.832 0.412 5.982 1.209 1.733 2.864 1.975 0.823 4.265 0.199 0.682 0.831
52.526 0.628 6.145 1.435 1.826 3.102 1.882 0.861 4.140 0.408 0.985 1.190
62.161 0.688 6.141 1.470 1.881 3.065 1.929 0.673 3.982 0.579 1.072 1.470
72.012 0.697 6.079 1.504 1.858 2.982 2.010 0.689 3.785 0.713 1.006 1.529
81.927 0.668 5.978 1.501 1.832 2.876 1.951 0.797 3.616 0.794 0.962 1.619
92.041 0.605 5.862 1.440 1.840 2.893 1.957 0.849 3.393 0.855 1.014 1.764
102.170 0.574 5.726 1.385 1.787 2.938 1.959 0.976 3.329 0.882 1.074 1.743
112.180 0.572 5.528 1.351 1.758 2.948 2.024 1.069 3.241 0.897 1.085 1.788
122.186 0.619 5.359 1.278 1.773 3.052 2.089 1.158 3.162 0.895 1.172 1.796
132.112 0.599 5.180 1.193 1.671 3.135 2.095 1.202 3.019 0.892 1.178 1.769
142.019 0.586 5.070 1.107 1.608 3.205 2.096 1.202 2.906 0.886 1.155 1.754
151.984 0.611 4.989 1.033 1.594 3.286 2.134 1.213 2.845 0.887 1.163 1.748
161.984 0.630 4.942 0.936 1.571 3.371 2.153 1.173 2.782 0.885 1.118 1.740
171.946 0.639 4.875 0.853 1.521 3.408 2.187 1.177 2.703 0.860 1.035 1.680
181.901 0.633 4.833 0.754 1.471 3.420 2.216 1.176 2.595 0.853 0.977 1.642
191.824 0.644 4.796 0.653 1.433 3.405 2.246 1.183 2.478 0.851 0.881 1.623
201.719 0.643 4.768 0.574 1.359 3.386 2.293 1.204 2.365 0.836 0.803 1.584
211.614 0.645 4.737 0.519 1.286 3.397 2.379 1.185 2.263 0.830 0.732 1.577
221.539 0.629 4.718 0.452 1.249 3.391 2.436 1.203 2.159 0.825 0.683 1.567
231.492 0.608 4.700 0.391 1.213 3.414 2.491 1.246 2.056 0.831 0.649 1.588
241.446 0.569 4.692 0.357 1.131 3.436 2.522 1.286 1.977 0.833 0.639 1.596
251.375 0.524 4.683 0.343 1.045 3.437 2.550 1.338 1.890 0.837 0.611 1.617
261.266 0.475 4.668 0.324 0.971 3.446 2.572 1.396 1.797 0.848 0.609 1.635
271.160 0.422 4.647 0.289 0.876 3.435 2.621 1.411 1.693 0.855 0.641 1.655
281.063 0.373 4.636 0.247 0.782 3.435 2.676 1.402 1.602 0.865 0.676 1.702
290.983 0.334 4.643 0.209 0.681 3.404 2.729 1.411 1.519 0.878 0.703 1.730
300.931 0.300 4.664 0.169 0.574 3.384 2.771 1.403 1.454 0.891 0.743 1.740
310.894 0.273 4.688 0.142 0.502 3.378 2.827 1.402 1.402 0.906 0.784 1.763
320.874 0.252 4.704 0.117 0.433 3.378 2.877 1.400 1.349 0.922 0.816 1.782
330.855 0.243 4.725 0.094 0.359 3.390 2.919 1.419 1.308 0.946 0.822 1.796
340.825 0.243 4.748 0.076 0.307 3.407 2.969 1.431 1.281 0.964 0.827 1.812
350.790 0.246 4.777 0.064 0.251 3.438 3.018 1.447 1.258 0.985 0.818 1.830
360.755 0.251 4.808 0.058 0.213 3.473 3.053 1.460 1.226 0.994 0.815 1.848
370.722 0.240 4.847 0.052 0.180 3.519 3.093 1.460 1.204 1.019 0.800 1.848
380.695 0.227 4.890 0.067 0.144 3.559 3.114 1.463 1.194 1.039 0.790 1.856
390.668 0.218 4.929 0.090 0.123 3.600 3.130 1.488 1.199 1.067 0.794 1.867
400.646 0.211 4.970 0.115 0.110 3.639 3.152 1.504 1.206 1.086 0.792 1.878
410.626 0.211 5.005 0.141 0.099 3.677 3.170 1.561 1.223 1.105 0.774 1.900
420.604 0.221 5.041 0.166 0.102 3.710 3.178 1.634 1.239 1.130 0.757 1.924
430.584 0.245 5.077 0.192 0.102 3.744 3.190 1.676 1.264 1.156 0.735 1.945
440.571 0.264 5.114 0.211 0.113 3.780 3.201 1.706 1.283 1.175 0.719 1.958
450.561 0.284 5.142 0.221 0.129 3.834 3.205 1.725 1.304 1.197 0.717 1.978
460.564 0.299 5.161 0.227 0.141 3.883 3.200 1.753 1.324 1.223 0.701 1.992
470.553 0.314 5.171 0.235 0.166 3.932 3.201 1.780 1.342 1.243 0.705 1.997
480.551 0.323 5.178 0.251 0.186 3.994 3.204 1.811 1.367 1.266 0.711 2.014
490.566 0.332 5.181 0.269 0.212 4.036 3.197 1.845 1.387 1.285 0.717 2.028
500.587 0.335 5.189 0.290 0.234 4.074 3.181 1.905 1.399 1.302 0.724 2.038
510.621 0.339 5.196 0.310 0.249 4.113 3.162 1.916 1.408 1.328 0.737 2.048
520.665 0.352 5.206 0.340 0.271 4.131 3.133 1.944 1.422 1.331 0.749 2.060


Data for figure immediately follows

Data for Appendix 3 - Random Walk Hypothesis Tests: Equity (Malaysia - Turkey)

qMalaysiaPhilippinesRussiaSingaporeTaiwanThailandIsraelKuwaitNigeriaSaudi ArabiaSouth AfricaTurkey
21.007 2.410 1.032 2.867 2.688 2.712 -0.649 2.306 -0.214 1.693 0.276 0.680
30.917 3.335 1.501 3.407 3.760 3.218 -0.102 2.523 0.523 1.388 0.649 1.114
41.275 3.930 1.865 3.591 3.955 3.698 0.028 2.950 0.759 1.541 0.930 1.246
51.411 4.062 1.789 3.556 3.963 3.702 0.054 3.083 0.817 1.598 0.995 1.198
61.660 4.066 1.914 3.636 3.936 3.625 0.152 3.107 0.979 1.608 1.120 1.149
71.838 3.973 1.975 3.660 3.724 3.619 0.355 2.943 0.947 1.570 1.153 0.997
82.026 3.911 2.045 3.766 3.698 3.602 0.336 3.049 0.955 1.454 1.019 0.880
92.219 3.841 2.014 3.769 3.604 3.477 0.251 3.169 1.003 1.377 0.984 0.783
102.380 3.715 2.026 3.654 3.547 3.308 0.164 3.273 1.100 1.355 0.982 0.732
112.474 3.554 2.029 3.575 3.444 3.200 0.105 3.402 1.151 1.393 0.940 0.642
122.514 3.447 2.039 3.541 3.351 3.081 0.088 3.449 1.187 1.476 0.966 0.593
132.530 3.324 2.079 3.493 3.294 2.958 0.070 3.374 1.133 1.529 0.918 0.555
142.514 3.232 2.129 3.443 3.228 2.873 0.069 3.298 1.158 1.595 0.928 0.536
152.478 3.123 2.161 3.341 3.158 2.794 0.106 3.233 1.176 1.656 0.964 0.530
162.436 3.018 2.153 3.212 3.085 2.702 0.119 3.187 1.177 1.673 0.963 0.528
172.415 2.934 2.177 3.113 3.046 2.632 0.102 3.141 1.191 1.705 0.942 0.552
182.376 2.818 2.226 3.019 2.982 2.549 0.099 3.118 1.216 1.728 0.946 0.563
192.314 2.696 2.272 2.934 2.909 2.433 0.048 3.150 1.218 1.749 0.906 0.555
202.271 2.564 2.345 2.857 2.899 2.310 0.020 3.194 1.225 1.790 0.823 0.526
212.228 2.414 2.393 2.778 2.877 2.181 -0.010 3.231 1.220 1.846 0.730 0.513
222.185 2.266 2.418 2.720 2.853 2.024 -0.027 3.221 1.237 1.908 0.626 0.476
232.142 2.134 2.449 2.673 2.821 1.887 -0.014 3.231 1.265 1.951 0.538 0.418
242.106 2.011 2.474 2.633 2.781 1.773 0.001 3.248 1.295 1.988 0.455 0.349
252.073 1.893 2.486 2.589 2.735 1.659 -0.029 3.227 1.335 1.991 0.392 0.297
262.035 1.769 2.493 2.546 2.691 1.551 -0.042 3.147 1.366 2.020 0.352 0.244
271.997 1.650 2.483 2.513 2.651 1.451 -0.047 3.137 1.421 2.068 0.315 0.197
281.942 1.533 2.466 2.467 2.596 1.360 -0.053 3.130 1.450 2.113 0.270 0.158
291.897 1.395 2.463 2.425 2.535 1.300 -0.059 3.132 1.472 2.161 0.219 0.124
301.852 1.292 2.458 2.379 2.483 1.246 -0.061 3.148 1.490 2.215 0.145 0.088
311.819 1.181 2.468 2.338 2.446 1.213 -0.083 3.134 1.518 2.257 0.097 0.059
321.803 1.080 2.485 2.311 2.407 1.187 -0.096 3.132 1.553 2.293 0.053 0.053
331.780 0.991 2.503 2.283 2.373 1.176 -0.118 3.138 1.587 2.332 0.019 0.041
341.768 0.914 2.532 2.264 2.333 1.184 -0.128 3.126 1.611 2.386 -0.009 0.041
351.760 0.848 2.561 2.248 2.279 1.189 -0.121 3.106 1.650 2.411 -0.032 0.038
361.745 0.798 2.600 2.221 2.233 1.193 -0.101 3.105 1.690 2.460 -0.056 0.032
371.739 0.773 2.629 2.190 2.180 1.196 -0.086 3.099 1.714 2.530 -0.087 0.024
381.741 0.752 2.647 2.162 2.134 1.199 -0.067 3.093 1.747 2.563 -0.108 0.020
391.738 0.733 2.661 2.139 2.088 1.202 -0.053 3.101 1.774 2.587 -0.114 0.023
401.742 0.710 2.668 2.120 2.044 1.212 -0.040 3.192 1.817 2.646 -0.109 0.021
411.749 0.686 2.673 2.096 2.010 1.217 -0.029 3.172 1.858 2.708 -0.099 0.022
421.752 0.672 2.680 2.069 1.979 1.233 -0.031 3.106 1.890 2.758 -0.085 0.031
431.760 0.662 2.686 2.046 1.957 1.254 -0.046 3.118 1.927 2.780 -0.081 0.047
441.764 0.651 2.681 2.018 1.932 1.271 -0.056 3.113 1.961 2.797 -0.070 0.061
451.774 0.638 2.685 2.004 1.916 1.293 -0.064 3.077 1.994 2.819 -0.066 0.086
461.792 0.623 2.695 1.993 1.904 1.313 -0.069 3.080 2.028 2.856 -0.060 0.110
471.799 0.610 2.700 1.974 1.888 1.329 -0.065 3.111 2.050 2.896 -0.055 0.136
481.804 0.600 2.709 1.960 1.873 1.346 -0.066 3.151 2.076 2.941 -0.051 0.161
491.809 0.586 2.705 1.954 1.855 1.361 -0.058 3.197 2.098 2.974 -0.039 0.180
501.818 0.577 2.693 1.957 1.841 1.370 -0.041 3.312 2.118 3.017 -0.027 0.197
511.828 0.569 2.682 1.964 1.835 1.372 -0.031 3.346 2.133 3.033 -0.016 0.212
521.835 0.564 2.677 1.972 1.836 1.376 -0.019 3.281 2.144 3.045 -0.012 0.221

Data for figure immediately follows

Data for Appendix 3 - Random Walk Hypothesis Tests: Equity (United Arab Emirates - Netherlands)

qUAEAustraliaBelgiumCanadaCzech RepublicDenmarkFranceGermanyHungaryItalyJapanNetherlands
22.654 1.758 -0.883 2.124 0.111 0.486 -2.063 -1.802 0.907 2.272 0.366 -1.023
33.184 2.479 -0.218 2.269 0.811 1.028 -1.359 -0.859 1.805 3.108 0.538 -0.083
43.252 2.818 0.171 2.636 1.553 1.175 -0.677 -0.268 2.366 4.058 1.067 0.224
53.129 2.757 0.229 2.788 1.563 1.194 -0.475 -0.119 2.553 4.335 1.304 0.303
63.113 2.648 0.235 2.811 1.720 1.196 -0.389 -0.050 2.715 4.249 1.511 0.299
73.055 2.399 0.308 2.794 1.930 1.122 -0.278 0.085 2.701 4.002 1.492 0.410
82.977 2.211 0.353 2.757 1.849 0.928 -0.234 0.180 2.596 3.607 1.594 0.431
92.979 2.002 0.390 2.642 1.674 0.917 -0.216 0.188 2.539 3.318 1.720 0.450
103.332 1.836 0.462 2.593 1.626 0.936 -0.192 0.214 2.359 3.180 1.851 0.485
113.556 1.681 0.479 2.530 1.504 0.945 -0.141 0.294 2.240 3.029 1.930 0.481
123.843 1.549 0.509 2.441 1.494 0.992 -0.018 0.381 2.176 2.901 1.980 0.533
134.029 1.447 0.511 2.372 1.379 0.984 0.012 0.413 2.073 2.795 1.999 0.526
144.211 1.370 0.508 2.351 1.313 1.021 0.078 0.464 2.034 2.840 2.002 0.516
154.416 1.312 0.496 2.308 1.308 1.073 0.136 0.501 1.979 2.925 2.034 0.519
164.561 1.272 0.481 2.274 1.281 1.123 0.164 0.533 1.949 2.980 2.088 0.513
174.681 1.238 0.483 2.225 1.221 1.140 0.182 0.549 1.925 2.990 2.133 0.492
184.857 1.205 0.492 2.211 1.158 1.155 0.180 0.575 1.895 3.049 2.188 0.474
195.020 1.169 0.507 2.187 1.129 1.174 0.180 0.584 1.860 3.095 2.230 0.438
205.187 1.133 0.511 2.145 1.080 1.194 0.161 0.586 1.822 3.081 2.240 0.393
215.372 1.098 0.511 2.123 1.057 1.212 0.150 0.588 1.782 3.046 2.254 0.353
225.546 1.069 0.511 2.106 1.051 1.235 0.134 0.595 1.756 3.008 2.271 0.313
235.766 1.036 0.537 2.110 1.106 1.299 0.143 0.621 1.731 2.985 2.304 0.296
245.972 1.007 0.559 2.118 1.108 1.380 0.162 0.642 1.719 2.981 2.353 0.280
256.198 0.987 0.572 2.137 1.107 1.462 0.192 0.672 1.729 2.987 2.357 0.270
266.427 0.955 0.597 2.154 1.113 1.551 0.226 0.707 1.745 2.979 2.371 0.268
276.607 0.931 0.604 2.188 1.141 1.620 0.260 0.739 1.768 2.993 2.380 0.259
286.769 0.909 0.623 2.211 1.168 1.681 0.297 0.776 1.797 3.020 2.373 0.260
296.957 0.889 0.621 2.219 1.184 1.738 0.315 0.796 1.837 3.029 2.363 0.249
307.150 0.873 0.616 2.235 1.199 1.768 0.322 0.792 1.867 3.034 2.340 0.222
317.342 0.847 0.616 2.260 1.216 1.787 0.337 0.799 1.898 3.049 2.328 0.198
327.532 0.827 0.621 2.257 1.232 1.815 0.350 0.805 1.942 3.072 2.318 0.182
337.704 0.804 0.614 2.258 1.244 1.837 0.358 0.814 1.960 3.091 2.313 0.165
347.877 0.787 0.626 2.263 1.255 1.868 0.379 0.831 1.993 3.103 2.307 0.163
358.025 0.772 0.638 2.260 1.257 1.886 0.395 0.841 2.013 3.104 2.280 0.156
368.172 0.751 0.641 2.255 1.253 1.894 0.407 0.847 2.035 3.105 2.268 0.143
378.315 0.738 0.650 2.256 1.261 1.908 0.419 0.844 2.047 3.105 2.255 0.133
388.447 0.726 0.656 2.257 1.256 1.919 0.426 0.838 2.062 3.096 2.245 0.125
398.575 0.717 0.673 2.260 1.247 1.937 0.440 0.842 2.067 3.094 2.244 0.123
408.687 0.706 0.690 2.271 1.251 1.956 0.453 0.838 2.077 3.109 2.243 0.124
418.819 0.705 0.709 2.276 1.250 1.973 0.471 0.839 2.080 3.125 2.245 0.129
428.954 0.702 0.728 2.279 1.249 1.987 0.486 0.843 2.092 3.147 2.254 0.140
439.079 0.693 0.743 2.283 1.257 2.009 0.499 0.837 2.093 3.162 2.266 0.154
449.212 0.683 0.765 2.286 1.267 2.036 0.518 0.838 2.094 3.182 2.278 0.176
459.334 0.662 0.785 2.288 1.285 2.065 0.543 0.844 2.100 3.212 2.296 0.201
469.437 0.646 0.806 2.291 1.304 2.100 0.569 0.847 2.110 3.230 2.318 0.229
479.570 0.626 0.825 2.296 1.323 2.142 0.593 0.849 2.114 3.238 2.334 0.253
489.685 0.611 0.848 2.294 1.355 2.180 0.617 0.858 2.126 3.251 2.350 0.275
499.781 0.605 0.874 2.294 1.373 2.208 0.645 0.864 2.128 3.277 2.368 0.297
509.870 0.604 0.898 2.299 1.387 2.224 0.670 0.871 2.127 3.308 2.382 0.314
519.972 0.606 0.918 2.297 1.425 2.230 0.692 0.875 2.126 3.330 2.394 0.329
5210.077 0.606 0.943 2.282 1.458 2.234 0.719 0.880 2.120 3.360 2.407 0.345

Data for figure immediately follows

Data for Appendix 3 - Random Walk Hypothesis Tests: Equity (Norway - United States)

qNorwayNew ZealandPolandSwedenSpainSwitzerlandUnited KingomUnited States
20.939 0.554 2.280 -1.379 -1.532 -1.324 0.357 -0.896
30.922 0.730 2.363 -0.933 -0.390 -0.679 0.889 -0.718
41.115 1.027 2.578 -0.618 0.097 -0.205 1.096 -0.450
51.480 1.192 2.379 -0.593 0.382 0.050 1.059 -0.408
61.605 1.126 2.412 -0.541 0.377 0.066 0.996 -0.432
71.613 0.974 2.433 -0.341 0.412 0.189 0.995 -0.341
81.567 0.741 2.536 -0.335 0.380 0.223 0.842 -0.314
91.558 0.554 2.642 -0.303 0.302 0.150 0.668 -0.414
101.634 0.396 2.696 -0.321 0.298 0.166 0.527 -0.424
111.662 0.273 2.820 -0.312 0.262 0.176 0.417 -0.458
121.715 0.229 2.906 -0.259 0.312 0.183 0.375 -0.469
131.711 0.171 2.983 -0.182 0.291 0.163 0.316 -0.469
141.762 0.137 3.055 -0.044 0.296 0.156 0.268 -0.426
151.825 0.117 3.109 0.070 0.304 0.157 0.229 -0.400
161.883 0.164 3.126 0.137 0.296 0.157 0.188 -0.386
171.906 0.156 3.110 0.197 0.274 0.169 0.160 -0.378
181.936 0.120 3.086 0.243 0.259 0.169 0.134 -0.381
191.963 0.082 3.044 0.301 0.260 0.140 0.109 -0.405
201.966 0.025 3.036 0.345 0.246 0.114 0.074 -0.427
211.938 -0.065 3.051 0.375 0.238 0.093 0.012 -0.442
221.929 -0.170 3.082 0.409 0.230 0.093 -0.028 -0.446
231.926 -0.258 3.131 0.466 0.237 0.122 -0.048 -0.425
241.910 -0.318 3.172 0.511 0.228 0.159 -0.054 -0.384
251.904 -0.355 3.215 0.560 0.218 0.199 -0.059 -0.358
261.912 -0.380 3.252 0.614 0.200 0.237 -0.066 -0.342
271.930 -0.381 3.297 0.669 0.194 0.277 -0.084 -0.321
281.952 -0.393 3.348 0.738 0.199 0.309 -0.088 -0.302
291.964 -0.410 3.397 0.791 0.196 0.323 -0.096 -0.285
301.956 -0.431 3.449 0.826 0.187 0.321 -0.104 -0.271
311.957 -0.437 3.502 0.862 0.196 0.324 -0.110 -0.259
321.970 -0.441 3.560 0.893 0.202 0.326 -0.117 -0.267
331.974 -0.451 3.612 0.929 0.208 0.327 -0.131 -0.271
341.986 -0.450 3.651 0.968 0.228 0.336 -0.135 -0.264
351.999 -0.445 3.697 0.998 0.239 0.344 -0.145 -0.268
362.016 -0.454 3.732 1.019 0.241 0.343 -0.167 -0.269
372.034 -0.456 3.764 1.037 0.239 0.342 -0.187 -0.263
382.053 -0.440 3.796 1.057 0.239 0.343 -0.221 -0.247
392.076 -0.424 3.835 1.089 0.249 0.346 -0.247 -0.233
402.113 -0.416 3.882 1.120 0.272 0.342 -0.271 -0.217
412.152 -0.400 3.925 1.158 0.293 0.347 -0.292 -0.208
422.186 -0.377 3.975 1.186 0.320 0.350 -0.313 -0.206
432.224 -0.351 4.020 1.207 0.340 0.350 -0.337 -0.205
442.261 -0.334 4.054 1.232 0.365 0.358 -0.354 -0.193
452.298 -0.314 4.087 1.257 0.390 0.373 -0.361 -0.179
462.333 -0.305 4.110 1.286 0.414 0.387 -0.363 -0.164
472.363 -0.305 4.131 1.318 0.436 0.402 -0.365 -0.145
482.392 -0.306 4.149 1.338 0.461 0.425 -0.364 -0.135
492.418 -0.310 4.159 1.355 0.486 0.446 -0.360 -0.123
502.436 -0.316 4.165 1.379 0.505 0.469 -0.356 -0.101
512.453 -0.321 4.164 1.401 0.522 0.487 -0.358 -0.082
522.468 -0.326 4.163 1.425 0.545 0.505 -0.363 -0.070

Data for figure immediately follows

Data for Appendix 3 - Random Walk Hypothesis Tests: Commodity (Crude Oil - Platinum)

qCrude OilNatural GasHeating OilGasolineAluminumCopperGoldLeadNickelSilverTinPlatinum
2-2.035 -1.265 -1.996 -1.519 -0.044 -0.950 0.560 1.188 -0.230 0.104 0.630 1.040
3-2.266 -1.302 -2.288 -2.217 0.966 -0.683 0.788 1.555 -0.657 -0.122 0.945 0.522
4-1.969 -0.920 -2.035 -2.081 1.398 -0.411 0.831 1.422 -0.395 0.060 1.066 0.493
5-1.312 -0.744 -2.015 -1.871 1.669 -0.262 0.940 1.287 -0.266 0.029 0.735 0.714
6-1.066 -0.636 -2.042 -1.582 1.586 -0.264 0.872 1.181 -0.279 -0.126 0.397 1.019
7-0.956 -0.663 -2.054 -1.595 1.554 -0.525 0.761 1.268 -0.248 -0.365 0.066 1.178
8-0.956 -0.820 -2.055 -1.704 1.465 -0.665 0.674 1.411 -0.181 -0.530 -0.137 1.110
9-0.835 -0.842 -1.943 -1.714 1.423 -0.685 0.600 1.690 -0.071 -0.610 -0.238 1.239
10-0.792 -0.935 -1.992 -1.688 1.327 -0.725 0.589 1.742 0.086 -0.626 -0.294 1.346
11-0.724 -0.987 -2.032 -1.654 1.249 -0.842 0.442 1.588 0.188 -0.745 -0.357 1.390
12-0.773 -1.070 -2.029 -1.666 1.224 -0.917 0.361 1.484 0.244 -0.800 -0.393 1.516
13-0.753 -1.144 -2.033 -1.659 1.130 -0.919 0.255 1.451 0.385 -0.813 -0.419 1.587
14-0.757 -1.192 -2.025 -1.698 1.091 -0.910 0.193 1.425 0.468 -0.815 -0.438 1.651
15-0.703 -1.223 -1.976 -1.660 1.047 -0.856 0.158 1.441 0.567 -0.726 -0.423 1.717
16-0.683 -1.215 -1.967 -1.598 1.003 -0.802 0.114 1.455 0.643 -0.647 -0.398 1.773
17-0.674 -1.216 -1.964 -1.560 0.975 -0.719 0.098 1.444 0.762 -0.517 -0.380 1.839
18-0.660 -1.234 -1.959 -1.544 0.946 -0.605 0.127 1.391 0.857 -0.374 -0.319 1.875
19-0.640 -1.186 -1.939 -1.466 0.900 -0.547 0.121 1.364 0.924 -0.281 -0.287 1.868
20-0.664 -1.160 -1.912 -1.413 0.853 -0.527 0.096 1.371 0.971 -0.236 -0.232 1.890
21-0.684 -1.157 -1.900 -1.412 0.811 -0.492 0.079 1.361 1.007 -0.207 -0.202 1.902
22-0.698 -1.144 -1.886 -1.406 0.767 -0.501 0.023 1.334 1.047 -0.200 -0.226 1.898
23-0.689 -1.140 -1.875 -1.393 0.742 -0.490 -0.033 1.310 1.110 -0.209 -0.250 1.913
24-0.705 -1.147 -1.874 -1.371 0.722 -0.469 -0.088 1.287 1.171 -0.210 -0.290 1.941
25-0.727 -1.178 -1.864 -1.339 0.676 -0.447 -0.146 1.274 1.237 -0.232 -0.324 1.965
26-0.754 -1.212 -1.854 -1.324 0.645 -0.409 -0.176 1.271 1.295 -0.237 -0.327 2.012
27-0.767 -1.231 -1.841 -1.315 0.625 -0.385 -0.218 1.297 1.337 -0.275 -0.350 2.050
28-0.792 -1.261 -1.819 -1.309 0.591 -0.354 -0.287 1.330 1.372 -0.315 -0.372 2.087
29-0.829 -1.282 -1.813 -1.307 0.560 -0.346 -0.351 1.355 1.389 -0.337 -0.408 2.115
30-0.862 -1.296 -1.801 -1.289 0.525 -0.357 -0.404 1.366 1.373 -0.362 -0.453 2.137
31-0.889 -1.315 -1.792 -1.264 0.488 -0.367 -0.443 1.370 1.370 -0.365 -0.483 2.168
32-0.899 -1.325 -1.791 -1.243 0.458 -0.371 -0.460 1.376 1.352 -0.368 -0.495 2.194
33-0.913 -1.333 -1.791 -1.217 0.431 -0.394 -0.463 1.384 1.359 -0.365 -0.496 2.204
34-0.930 -1.334 -1.790 -1.184 0.406 -0.409 -0.461 1.408 1.383 -0.368 -0.489 2.240
35-0.945 -1.336 -1.789 -1.161 0.373 -0.441 -0.449 1.432 1.395 -0.369 -0.480 2.280
36-0.953 -1.344 -1.785 -1.149 0.339 -0.475 -0.445 1.458 1.409 -0.388 -0.479 2.325
37-0.961 -1.342 -1.790 -1.130 0.301 -0.505 -0.441 1.472 1.415 -0.421 -0.478 2.364
38-0.972 -1.344 -1.795 -1.109 0.252 -0.535 -0.431 1.471 1.419 -0.446 -0.478 2.372
39-0.974 -1.361 -1.806 -1.100 0.197 -0.554 -0.420 1.456 1.402 -0.469 -0.478 2.381
40-0.975 -1.377 -1.824 -1.083 0.151 -0.559 -0.409 1.436 1.406 -0.478 -0.477 2.383
41-0.972 -1.390 -1.842 -1.074 0.104 -0.562 -0.389 1.413 1.414 -0.501 -0.486 2.394
42-0.967 -1.406 -1.855 -1.056 0.060 -0.575 -0.362 1.393 1.429 -0.509 -0.479 2.406
43-0.962 -1.432 -1.857 -1.048 0.015 -0.580 -0.345 1.352 1.446 -0.509 -0.453 2.394
44-0.960 -1.451 -1.869 -1.043 -0.037 -0.592 -0.335 1.294 1.453 -0.512 -0.429 2.374
45-0.951 -1.455 -1.871 -1.019 -0.075 -0.606 -0.325 1.238 1.460 -0.519 -0.411 2.363
46-0.940 -1.459 -1.849 -0.998 -0.103 -0.624 -0.301 1.183 1.476 -0.521 -0.383 2.362
47-0.931 -1.448 -1.846 -0.972 -0.128 -0.640 -0.276 1.132 1.500 -0.520 -0.358 2.364
48-0.914 -1.431 -1.838 -0.939 -0.139 -0.647 -0.251 1.094 1.524 -0.525 -0.343 2.366
49-0.896 -1.406 -1.820 -0.905 -0.124 -0.654 -0.213 1.056 1.566 -0.523 -0.327 2.380
50-0.876 -1.371 -1.806 -0.856 -0.098 -0.664 -0.172 1.032 1.604 -0.516 -0.306 2.409
51-0.862 -1.344 -1.794 -0.835 -0.066 -0.669 -0.139 0.997 1.635 -0.500 -0.280 2.440
52-0.848 -1.315 -1.772 -0.810 -0.031 -0.683 -0.109 0.960 1.673 -0.501 -0.262 2.468

Data for figure immediately follows

Data for Appendix 3 - Random Walk Hypothesis Tests: Commodity (Silver - Sugar)

qZincCattleCocoaCoffeeCornCottonRubberSoybeansSugarWheat
2-0.638 1.630 5.417 0.083 -1.853 1.565 -0.589 -0.971 -1.178 1.785
3-0.579 1.978 5.864 0.189 -1.724 1.818 -1.706 -1.518 -1.036 1.110
4-0.314 1.871 5.905 0.688 -1.564 1.863 -1.732 -1.853 -1.081 0.864
5-0.197 1.527 5.551 1.030 -1.683 1.674 -1.452 -1.901 -0.993 0.863
6-0.323 1.115 5.035 1.350 -1.724 1.547 -1.388 -1.906 -0.932 0.960
7-0.491 0.631 4.534 1.317 -1.691 1.465 -1.515 -1.825 -0.962 0.984
8-0.562 0.298 4.175 1.425 -1.711 1.570 -1.284 -1.822 -0.954 1.038
9-0.631 -0.084 3.845 1.527 -1.686 1.688 -1.117 -1.814 -1.012 1.032
10-0.717 -0.225 3.575 1.538 -1.698 1.862 -1.113 -1.976 -0.988 1.020
11-0.906 -0.334 3.399 1.582 -1.653 2.029 -1.079 -2.019 -0.943 1.112
12-1.027 -0.422 3.289 1.600 -1.597 2.168 -1.088 -2.004 -0.827 1.162
13-1.129 -0.456 3.237 1.634 -1.575 2.252 -1.119 -1.975 -0.749 1.171
14-1.212 -0.497 3.196 1.652 -1.546 2.288 -1.197 -2.004 -0.587 1.185
15-1.197 -0.496 3.124 1.714 -1.532 2.333 -1.212 -1.991 -0.447 1.290
16-1.178 -0.471 3.025 1.746 -1.515 2.396 -1.190 -1.940 -0.337 1.359
17-1.138 -0.428 2.916 1.776 -1.477 2.481 -1.203 -1.876 -0.282 1.404
18-1.047 -0.340 2.797 1.819 -1.463 2.577 -1.233 -1.827 -0.228 1.465
19-0.991 -0.257 2.676 1.803 -1.457 2.644 -1.283 -1.743 -0.176 1.543
20-0.965 -0.177 2.549 1.749 -1.439 2.697 -1.320 -1.693 -0.171 1.616
21-0.935 -0.122 2.432 1.713 -1.417 2.735 -1.336 -1.633 -0.172 1.688
22-0.905 -0.098 2.333 1.671 -1.379 2.769 -1.368 -1.619 -0.212 1.749
23-0.899 -0.084 2.261 1.604 -1.322 2.798 -1.383 -1.582 -0.231 1.778
24-0.903 -0.047 2.189 1.525 -1.283 2.802 -1.406 -1.551 -0.255 1.824
25-0.942 -0.032 2.099 1.430 -1.252 2.789 -1.421 -1.565 -0.264 1.886
26-0.971 -0.018 2.012 1.352 -1.212 2.767 -1.427 -1.571 -0.275 1.934
27-1.018 0.001 1.905 1.259 -1.174 2.728 -1.441 -1.557 -0.285 1.978
28-1.053 0.033 1.778 1.173 -1.153 2.698 -1.451 -1.572 -0.313 1.987
29-1.079 0.061 1.647 1.103 -1.135 2.650 -1.463 -1.579 -0.350 1.984
30-1.102 0.105 1.541 1.042 -1.125 2.598 -1.458 -1.571 -0.385 1.979
31-1.112 0.162 1.455 0.990 -1.124 2.545 -1.449 -1.562 -0.427 2.002
32-1.120 0.217 1.389 0.923 -1.127 2.474 -1.437 -1.556 -0.470 2.057
33-1.103 0.270 1.349 0.857 -1.127 2.401 -1.425 -1.516 -0.507 2.104
34-1.088 0.332 1.316 0.787 -1.123 2.353 -1.428 -1.474 -0.556 2.137
35-1.053 0.403 1.284 0.740 -1.104 2.319 -1.418 -1.432 -0.600 2.161
36-1.035 0.467 1.257 0.674 -1.090 2.274 -1.409 -1.411 -0.634 2.198
37-1.026 0.517 1.242 0.618 -1.073 2.228 -1.406 -1.397 -0.666 2.214
38-1.021 0.554 1.234 0.563 -1.049 2.206 -1.393 -1.390 -0.685 2.210
39-1.011 0.548 1.223 0.505 -1.042 2.191 -1.379 -1.376 -0.704 2.205
40-0.998 0.527 1.205 0.453 -1.051 2.165 -1.362 -1.383 -0.728 2.198
41-1.002 0.497 1.182 0.404 -1.056 2.127 -1.347 -1.383 -0.750 2.204
42-0.997 0.449 1.143 0.355 -1.061 2.087 -1.337 -1.392 -0.765 2.201
43-0.989 0.408 1.106 0.324 -1.056 2.040 -1.333 -1.403 -0.781 2.190
44-0.992 0.366 1.069 0.285 -1.050 1.987 -1.332 -1.414 -0.798 2.183
45-1.000 0.326 1.033 0.256 -1.038 1.934 -1.322 -1.413 -0.819 2.170
46-1.001 0.305 0.992 0.231 -1.031 1.882 -1.310 -1.412 -0.826 2.153
47-0.996 0.294 0.939 0.215 -1.034 1.842 -1.304 -1.399 -0.821 2.138
48-0.995 0.273 0.878 0.200 -1.045 1.808 -1.295 -1.387 -0.810 2.121
49-0.981 0.264 0.822 0.179 -1.050 1.776 -1.289 -1.359 -0.800 2.106
50-0.963 0.258 0.780 0.172 -1.052 1.758 -1.284 -1.329 -0.786 2.101
51-0.940 0.257 0.742 0.168 -1.046 1.745 -1.277 -1.305 -0.765 2.081
52-0.938 0.262 0.710 0.170 -1.042 1.729 -1.274 -1.287 -0.742 2.064

Data for figure immediately follows

Data for Appendix 3 - Random Walk Hypothesis Tests: USD Bilateral Exchange Rate (Argentina - Russia)

qArgentinaBrazilChileColombiaMexicoPeruIndonesiaIndiaSouth KoreaMalaysiaPhilippinesRussia
20.190 -1.755 1.564 0.634 -2.025 -0.109 0.430 -2.637 -0.318 -0.724 -1.266 -1.290
30.438 -1.221 1.615 1.579 -1.018 0.539 0.373 -1.955 0.767 -0.515 -0.640 -0.727
40.856 -0.794 1.989 2.104 -0.810 0.738 0.483 -1.620 0.974 -0.503 -0.504 -0.389
50.994 -0.636 2.137 2.268 -0.805 1.066 0.607 -1.218 1.214 -0.238 -0.252 -0.323
61.111 -0.459 2.463 2.235 -0.766 1.056 0.657 -0.946 1.312 0.065 -0.147 -0.160
71.113 -0.747 2.478 2.118 -0.758 1.048 0.803 -0.649 1.418 0.041 -0.002 -0.148
80.961 -0.650 2.510 2.043 -0.776 0.960 0.873 -0.485 1.464 -0.024 0.125 -0.058
91.006 -0.512 2.555 1.900 -0.877 0.886 0.901 -0.329 1.513 0.005 0.211 0.055
101.137 -0.477 2.403 1.931 -0.897 0.829 0.900 -0.259 1.514 0.030 0.329 0.169
111.105 -0.395 2.275 1.970 -0.952 0.839 0.915 -0.103 1.520 -0.060 0.399 0.210
121.171 -0.334 2.234 2.009 -0.944 0.799 0.875 -0.025 1.529 -0.116 0.525 0.150
131.146 -0.266 2.195 2.023 -1.014 0.797 0.845 0.060 1.512 -0.123 0.601 0.189
141.144 -0.225 2.234 2.030 -1.022 0.820 0.809 0.139 1.493 -0.095 0.674 0.177
151.110 -0.185 2.276 2.016 -1.059 0.838 0.760 0.216 1.463 -0.125 0.716 0.175
161.028 -0.134 2.301 1.955 -1.065 0.816 0.726 0.327 1.420 -0.200 0.743 0.199
170.920 -0.103 2.327 1.913 -1.083 0.784 0.719 0.409 1.379 -0.183 0.773 0.248
180.905 -0.053 2.352 1.892 -1.092 0.761 0.679 0.490 1.343 -0.155 0.782 0.295
190.869 0.014 2.402 1.884 -1.054 0.738 0.628 0.543 1.301 -0.145 0.777 0.315
200.770 0.081 2.442 1.905 -1.036 0.724 0.576 0.599 1.266 -0.154 0.753 0.340
210.739 0.135 2.479 1.948 -0.974 0.689 0.509 0.655 1.232 -0.166 0.711 0.390
220.717 0.180 2.512 1.994 -0.936 0.679 0.482 0.699 1.198 -0.201 0.666 0.437
230.710 0.230 2.517 2.032 -0.899 0.672 0.388 0.741 1.178 -0.237 0.641 0.488
240.680 0.272 2.496 2.080 -0.868 0.672 0.292 0.790 1.158 -0.283 0.610 0.546
250.643 0.309 2.455 2.113 -0.849 0.646 0.249 0.831 1.141 -0.309 0.585 0.601
260.617 0.347 2.434 2.101 -0.859 0.629 0.246 0.857 1.133 -0.362 0.554 0.648
270.601 0.387 2.388 2.090 -0.852 0.582 0.224 0.888 1.121 -0.455 0.523 0.680
280.600 0.413 2.338 2.086 -0.854 0.524 0.201 0.920 1.111 -0.549 0.498 0.697
290.595 0.421 2.279 2.083 -0.847 0.463 0.181 0.944 1.101 -0.622 0.491 0.723
300.586 0.420 2.207 2.101 -0.851 0.380 0.158 0.966 1.086 -0.696 0.500 0.743
310.576 0.415 2.149 2.131 -0.844 0.307 0.139 0.987 1.072 -0.743 0.506 0.763
320.561 0.412 2.103 2.153 -0.822 0.238 0.143 1.007 1.052 -0.807 0.510 0.779
330.542 0.407 2.061 2.193 -0.814 0.189 0.139 1.031 1.032 -0.851 0.528 0.803
340.502 0.403 2.035 2.235 -0.804 0.115 0.137 1.066 1.014 -0.884 0.551 0.823
350.469 0.399 2.016 2.269 -0.785 0.075 0.146 1.079 0.994 -0.935 0.571 0.828
360.449 0.396 1.988 2.306 -0.760 0.043 0.156 1.125 0.980 -0.981 0.598 0.839
370.427 0.392 1.955 2.329 -0.739 -0.016 0.167 1.167 0.970 -1.041 0.611 0.850
380.410 0.382 1.938 2.359 -0.706 -0.050 0.177 1.220 0.961 -1.061 0.635 0.865
390.401 0.377 1.923 2.384 -0.671 -0.060 0.157 1.275 0.960 -1.088 0.654 0.875
400.380 0.370 1.907 2.415 -0.624 -0.064 0.129 1.318 0.962 -1.110 0.684 0.876
410.367 0.366 1.882 2.441 -0.584 -0.059 0.113 1.370 0.967 -1.116 0.711 0.895
420.354 0.362 1.863 2.471 -0.539 -0.054 0.089 1.420 0.976 -1.092 0.746 0.904
430.328 0.358 1.851 2.509 -0.506 -0.042 0.046 1.461 0.986 -1.064 0.763 0.922
440.307 0.353 1.830 2.542 -0.477 -0.025 -0.008 1.504 0.994 -1.044 0.781 0.939
450.282 0.350 1.813 2.575 -0.452 -0.005 -0.058 1.539 1.001 -1.029 0.792 0.957
460.260 0.344 1.799 2.604 -0.433 -0.003 -0.107 1.575 1.008 -1.011 0.806 0.979
470.243 0.339 1.785 2.628 -0.418 -0.007 -0.161 1.603 1.014 -0.996 0.821 0.997
480.227 0.331 1.783 2.651 -0.403 -0.026 -0.207 1.631 1.021 -0.967 0.838 1.014
490.216 0.324 1.783 2.662 -0.384 -0.036 -0.253 1.664 1.027 -0.944 0.857 1.027
500.216 0.315 1.786 2.672 -0.373 -0.042 -0.290 1.698 1.031 -0.907 0.876 1.042
510.198 0.305 1.808 2.681 -0.360 -0.054 -0.322 1.731 1.032 -0.884 0.894 1.056
520.189 0.295 1.828 2.688 -0.350 -0.064 -0.356 1.757 1.032 -0.889 0.914 1.061

Data for figure immediately follows

Data for Appendix 3 - Random Walk Hypothesis Tests: USD Bilateral Exchange Rate (Singapore - Norway)

qSingaporeThailandIsraelNigeriaSouth AfricaTurkeyAustraliaCanadaCzech RepublicEuro AreaJapanNorway
20.570 0.004 1.172 -2.602 -0.183 -0.252 -0.757 0.549 1.011 0.214 2.472 0.944
31.329 0.326 2.052 -2.702 0.182 0.330 -0.189 0.842 1.276 0.016 3.550 1.332
41.484 0.684 2.387 -2.630 0.462 0.983 -0.426 0.571 0.909 0.097 3.954 1.304
51.691 0.872 2.572 -2.628 0.708 0.929 -0.181 0.550 0.807 0.288 4.218 1.305
61.808 0.956 2.652 -2.552 0.806 0.739 -0.140 0.443 0.962 0.588 4.216 1.491
71.750 1.153 2.619 -2.450 0.797 0.572 -0.023 0.418 1.009 0.681 4.111 1.413
81.739 1.220 2.580 -2.361 0.862 0.384 0.027 0.471 1.084 0.721 3.998 1.359
91.716 1.147 2.635 -2.239 0.962 0.262 0.035 0.455 1.043 0.700 3.913 1.410
101.634 1.179 2.585 -2.246 0.957 0.285 0.027 0.470 1.036 0.699 3.843 1.437
111.575 1.080 2.498 -2.246 0.958 0.331 -0.013 0.422 1.002 0.678 3.681 1.494
121.545 1.034 2.356 -2.195 1.003 0.401 -0.062 0.353 0.992 0.668 3.604 1.499
131.491 0.968 2.178 -2.195 1.055 0.435 -0.099 0.300 0.989 0.631 3.584 1.486
141.439 0.970 2.046 -2.125 1.100 0.459 -0.095 0.302 1.028 0.591 3.617 1.481
151.363 0.935 1.926 -2.114 1.164 0.517 -0.063 0.313 1.055 0.535 3.627 1.472
161.313 0.874 1.832 -2.113 1.177 0.532 -0.067 0.278 1.058 0.446 3.623 1.454
171.260 0.806 1.751 -2.098 1.178 0.516 -0.043 0.318 1.055 0.396 3.632 1.441
181.184 0.716 1.705 -2.111 1.194 0.512 -0.035 0.345 1.033 0.362 3.639 1.428
191.115 0.668 1.637 -2.115 1.214 0.499 -0.034 0.391 1.014 0.344 3.637 1.395
201.024 0.633 1.594 -2.120 1.212 0.484 -0.075 0.416 0.974 0.303 3.610 1.344
210.950 0.597 1.568 -2.111 1.192 0.471 -0.095 0.452 0.958 0.284 3.609 1.325
220.869 0.530 1.552 -2.088 1.165 0.431 -0.122 0.496 0.963 0.258 3.596 1.323
230.807 0.491 1.550 -2.070 1.118 0.392 -0.129 0.542 0.979 0.261 3.557 1.329
240.734 0.401 1.516 -2.053 1.071 0.342 -0.143 0.594 0.976 0.237 3.504 1.307
250.656 0.342 1.494 -2.051 1.050 0.251 -0.153 0.629 0.968 0.206 3.459 1.278
260.617 0.275 1.475 -2.040 1.018 0.190 -0.162 0.644 0.978 0.203 3.420 1.253
270.560 0.143 1.454 -2.029 0.970 0.148 -0.166 0.646 0.972 0.170 3.363 1.211
280.513 0.046 1.426 -2.015 0.929 0.120 -0.154 0.656 0.979 0.153 3.282 1.176
290.471 -0.063 1.396 -2.001 0.873 0.088 -0.153 0.659 0.981 0.144 3.191 1.145
300.437 -0.185 1.375 -1.987 0.817 0.045 -0.145 0.658 0.975 0.151 3.098 1.120
310.417 -0.258 1.327 -1.975 0.768 -0.007 -0.121 0.665 0.967 0.175 3.020 1.102
320.397 -0.279 1.267 -1.959 0.745 -0.064 -0.100 0.650 0.963 0.188 2.944 1.075
330.378 -0.304 1.226 -1.951 0.732 -0.128 -0.081 0.642 0.964 0.198 2.881 1.061
340.369 -0.302 1.179 -1.932 0.719 -0.200 -0.058 0.642 0.983 0.231 2.821 1.051
350.361 -0.311 1.146 -1.921 0.718 -0.257 -0.031 0.653 0.992 0.271 2.758 1.050
360.365 -0.316 1.143 -1.894 0.729 -0.315 0.002 0.661 0.998 0.300 2.712 1.054
370.380 -0.300 1.141 -1.869 0.736 -0.361 0.030 0.676 1.000 0.330 2.678 1.056
380.385 -0.272 1.157 -1.853 0.743 -0.389 0.071 0.685 1.003 0.366 2.656 1.050
390.396 -0.248 1.173 -1.830 0.751 -0.410 0.116 0.693 1.010 0.407 2.651 1.040
400.405 -0.233 1.201 -1.805 0.766 -0.421 0.155 0.702 1.013 0.452 2.641 1.032
410.419 -0.219 1.238 -1.767 0.782 -0.420 0.190 0.720 1.020 0.500 2.635 1.027
420.436 -0.201 1.293 -1.740 0.804 -0.423 0.220 0.728 1.020 0.546 2.638 1.028
430.452 -0.188 1.352 -1.718 0.822 -0.436 0.250 0.729 1.027 0.587 2.636 1.032
440.473 -0.177 1.407 -1.698 0.845 -0.450 0.278 0.739 1.033 0.626 2.630 1.036
450.487 -0.168 1.443 -1.680 0.865 -0.462 0.306 0.749 1.034 0.663 2.619 1.036
460.505 -0.162 1.477 -1.662 0.885 -0.457 0.333 0.762 1.042 0.707 2.612 1.044
470.524 -0.157 1.502 -1.637 0.898 -0.449 0.367 0.784 1.051 0.746 2.611 1.051
480.544 -0.163 1.509 -1.625 0.912 -0.436 0.397 0.804 1.062 0.781 2.616 1.056
490.559 -0.179 1.519 -1.609 0.938 -0.425 0.427 0.824 1.075 0.824 2.623 1.071
500.571 -0.184 1.524 -1.594 0.968 -0.414 0.457 0.845 1.091 0.861 2.639 1.082
510.584 -0.192 1.531 -1.584 0.997 -0.409 0.485 0.871 1.111 0.904 2.662 1.096
520.594 -0.199 1.543 -1.569 1.025 -0.414 0.512 0.890 1.123 0.937 2.685 1.104

Data for figure immediately follows

Data for Appendix 3 - Random Walk Hypothesis Tests: USD Bilateral Exchange Rate (New Zealand - United Kingdom)

qNew ZealandPolandSwedenSwitzerlandUnited Kingdom
20.039 -0.166 0.252 1.933 1.696
30.806 -0.034 1.072 2.194 1.620
40.898 0.352 1.369 2.187 1.452
51.077 0.454 1.855 2.372 1.564
61.200 0.654 2.304 2.513 1.783
71.293 0.777 2.576 2.492 1.902
81.373 0.777 2.692 2.348 2.008
91.354 0.727 2.680 2.340 2.115
101.315 0.646 2.691 2.369 2.119
111.222 0.583 2.714 2.346 2.047
121.211 0.518 2.719 2.310 1.997
131.264 0.461 2.702 2.313 1.942
141.339 0.428 2.714 2.326 1.903
151.404 0.386 2.716 2.325 1.874
161.458 0.366 2.689 2.329 1.900
171.534 0.348 2.708 2.323 1.916
181.597 0.368 2.741 2.293 1.899
191.611 0.382 2.742 2.265 1.880
201.597 0.347 2.730 2.219 1.879
211.581 0.320 2.749 2.199 1.905
221.570 0.310 2.774 2.176 1.925
231.561 0.308 2.793 2.138 1.936
241.564 0.300 2.806 2.106 1.930
251.568 0.308 2.810 2.070 1.911
261.582 0.323 2.799 2.039 1.883
271.585 0.338 2.764 1.994 1.865
281.602 0.361 2.732 1.937 1.851
291.610 0.386 2.703 1.879 1.839
301.631 0.409 2.667 1.836 1.821
311.675 0.449 2.644 1.812 1.794
321.721 0.481 2.610 1.779 1.762
331.763 0.515 2.589 1.747 1.722
341.790 0.564 2.584 1.727 1.691
351.833 0.622 2.586 1.712 1.667
361.884 0.664 2.596 1.701 1.647
371.931 0.691 2.617 1.687 1.636
381.994 0.705 2.635 1.680 1.629
392.062 0.714 2.644 1.671 1.617
402.123 0.726 2.662 1.668 1.606
412.191 0.736 2.680 1.668 1.605
422.245 0.741 2.710 1.674 1.603
432.299 0.741 2.739 1.682 1.601
442.343 0.739 2.771 1.697 1.599
452.392 0.739 2.797 1.712 1.591
462.436 0.737 2.835 1.731 1.582
472.496 0.736 2.868 1.740 1.571
482.546 0.728 2.896 1.748 1.560
492.581 0.720 2.933 1.764 1.564
502.619 0.724 2.962 1.775 1.572
512.653 0.731 2.991 1.787 1.582
522.684 0.741 3.014 1.797 1.592


Appendix 4.  Long Memory Hypothesis Tests

For all figures in Appendix 4, the 95% critical values are 0.809 (lower) and 1.862 (upper), and the 99% critical values are 0.721 (lower) and 2.098 (upper). The critical values do not depend upon xi.

Data for figure immediately follows

Data for Appendix 4 - Long Memory Hypothesis Tests: Equity (Argentina - South Korea)

xiArgentinaBrazilChileColombiaMexicoPeruVenezuelaChinaHong KongIndonesiaIndiaSouth Korea
01.511 1.330 2.294 1.744 1.411 2.614 1.394 1.376 1.392 1.878 1.494 1.865
11.506 1.307 2.148 1.675 1.398 2.511 1.348 1.378 1.397 1.764 1.479 1.860
21.504 1.303 2.067 1.641 1.399 2.468 1.330 1.378 1.386 1.708 1.471 1.861
31.501 1.306 2.008 1.621 1.394 2.441 1.308 1.373 1.369 1.679 1.460 1.864
41.503 1.311 1.960 1.612 1.389 2.420 1.281 1.372 1.363 1.667 1.454 1.878
51.498 1.319 1.920 1.618 1.384 2.405 1.263 1.374 1.355 1.665 1.453 1.892
61.481 1.328 1.888 1.626 1.381 2.393 1.252 1.380 1.347 1.667 1.455 1.901
71.467 1.331 1.860 1.632 1.379 2.379 1.242 1.386 1.340 1.669 1.459 1.905
81.457 1.329 1.836 1.638 1.380 2.359 1.230 1.394 1.335 1.670 1.459 1.911
91.445 1.319 1.813 1.641 1.377 2.334 1.215 1.400 1.327 1.668 1.457 1.911
101.437 1.308 1.793 1.642 1.375 2.308 1.206 1.407 1.319 1.664 1.456 1.906
111.432 1.300 1.775 1.646 1.371 2.287 1.199 1.411 1.312 1.657 1.457 1.903
121.427 1.295 1.758 1.645 1.366 2.266 1.192 1.415 1.303 1.648 1.457 1.902
131.422 1.291 1.741 1.639 1.361 2.243 1.186 1.418 1.293 1.638 1.455 1.898
141.417 1.286 1.723 1.631 1.354 2.222 1.181 1.416 1.286 1.631 1.454 1.892
151.414 1.283 1.707 1.622 1.347 2.204 1.178 1.415 1.281 1.624 1.452 1.886
161.412 1.282 1.693 1.613 1.342 2.188 1.176 1.412 1.276 1.616 1.449 1.880
171.411 1.281 1.681 1.603 1.338 2.172 1.173 1.409 1.272 1.608 1.446 1.874
181.411 1.280 1.670 1.591 1.334 2.154 1.171 1.409 1.269 1.600 1.443 1.868
191.412 1.277 1.659 1.582 1.329 2.138 1.170 1.407 1.266 1.592 1.440 1.864
201.411 1.273 1.649 1.575 1.324 2.124 1.170 1.409 1.265 1.584 1.437 1.861
211.409 1.270 1.640 1.570 1.320 2.111 1.169 1.409 1.264 1.577 1.435 1.855
221.408 1.265 1.631 1.565 1.315 2.101 1.168 1.410 1.263 1.570 1.433 1.850
231.409 1.262 1.623 1.558 1.312 2.091 1.167 1.412 1.261 1.563 1.430 1.843
241.411 1.259 1.616 1.552 1.309 2.082 1.167 1.416 1.259 1.555 1.427 1.836
251.416 1.256 1.609 1.547 1.306 2.074 1.166 1.418 1.258 1.548 1.424 1.831
261.419 1.254 1.602 1.543 1.303 2.066 1.166 1.422 1.257 1.541 1.422 1.826
271.420 1.252 1.596 1.539 1.301 2.057 1.165 1.425 1.256 1.535 1.420 1.822
281.423 1.251 1.590 1.536 1.299 2.046 1.163 1.427 1.255 1.529 1.418 1.817
291.427 1.249 1.584 1.532 1.298 2.036 1.161 1.427 1.255 1.524 1.416 1.811
301.431 1.248 1.578 1.527 1.298 2.028 1.160 1.428 1.254 1.519 1.415 1.805
311.433 1.247 1.573 1.522 1.298 2.021 1.159 1.428 1.254 1.515 1.414 1.801
321.434 1.245 1.568 1.520 1.297 2.016 1.157 1.428 1.253 1.511 1.413 1.797
331.436 1.245 1.564 1.518 1.296 2.012 1.157 1.426 1.253 1.507 1.413 1.794
341.438 1.244 1.559 1.516 1.295 2.008 1.156 1.424 1.252 1.504 1.413 1.791
351.438 1.245 1.554 1.515 1.295 2.004 1.157 1.421 1.251 1.501 1.413 1.787
361.439 1.246 1.550 1.515 1.294 2.001 1.157 1.418 1.251 1.499 1.412 1.783
371.441 1.247 1.547 1.514 1.294 1.998 1.157 1.417 1.250 1.496 1.412 1.778
381.443 1.248 1.545 1.513 1.293 1.995 1.158 1.416 1.250 1.494 1.411 1.774
391.444 1.250 1.542 1.513 1.293 1.992 1.158 1.414 1.250 1.493 1.410 1.770
401.445 1.252 1.539 1.514 1.293 1.990 1.158 1.412 1.250 1.491 1.409 1.766
411.444 1.253 1.535 1.514 1.292 1.987 1.158 1.409 1.250 1.489 1.407 1.762
421.444 1.253 1.532 1.514 1.291 1.984 1.157 1.406 1.250 1.486 1.404 1.758
431.445 1.253 1.528 1.513 1.290 1.981 1.157 1.404 1.249 1.484 1.402 1.755
441.445 1.252 1.525 1.512 1.290 1.978 1.156 1.402 1.249 1.482 1.399 1.752
451.445 1.252 1.522 1.512 1.289 1.975 1.156 1.399 1.248 1.480 1.396 1.749
461.445 1.252 1.519 1.510 1.289 1.972 1.155 1.397 1.247 1.479 1.393 1.746
471.446 1.253 1.516 1.510 1.289 1.969 1.154 1.395 1.246 1.478 1.390 1.743
481.447 1.253 1.514 1.509 1.290 1.965 1.154 1.394 1.245 1.477 1.387 1.739
491.447 1.253 1.512 1.509 1.290 1.962 1.153 1.392 1.244 1.476 1.384 1.736
501.447 1.253 1.511 1.509 1.290 1.959 1.152 1.391 1.243 1.475 1.381 1.733
511.447 1.253 1.509 1.508 1.290 1.956 1.150 1.390 1.242 1.474 1.379 1.729
521.447 1.253 1.509 1.507 1.290 1.953 1.149 1.388 1.241 1.473 1.376 1.726
531.447 1.251 1.507 1.507 1.290 1.950 1.147 1.386 1.240 1.472 1.374 1.723
541.449 1.250 1.506 1.506 1.289 1.946 1.145 1.384 1.240 1.471 1.372 1.719
551.452 1.248 1.505 1.507 1.289 1.942 1.144 1.382 1.239 1.471 1.370 1.716
561.455 1.247 1.503 1.508 1.288 1.938 1.143 1.380 1.239 1.471 1.368 1.714
571.457 1.247 1.502 1.509 1.288 1.933 1.142 1.379 1.238 1.471 1.366 1.711
581.460 1.247 1.501 1.512 1.288 1.929 1.142 1.378 1.237 1.470 1.364 1.709
591.462 1.247 1.500 1.514 1.289 1.924 1.141 1.378 1.237 1.470 1.363 1.707
601.465 1.247 1.499 1.517 1.290 1.920 1.140 1.378 1.237 1.470 1.362 1.705
611.468 1.246 1.498 1.519 1.291 1.915 1.139 1.377 1.236 1.469 1.361 1.704
621.471 1.245 1.498 1.521 1.292 1.911 1.139 1.376 1.236 1.469 1.361 1.703
631.472 1.245 1.497 1.523 1.294 1.908 1.138 1.375 1.237 1.468 1.361 1.701
641.474 1.244 1.496 1.525 1.295 1.904 1.137 1.375 1.237 1.467 1.360 1.699
651.476 1.243 1.495 1.526 1.295 1.901 1.136 1.375 1.236 1.467 1.360 1.697
661.478 1.243 1.494 1.528 1.296 1.897 1.135 1.375 1.236 1.466 1.359 1.695
671.480 1.243 1.492 1.529 1.296 1.894 1.134 1.374 1.235 1.465 1.359 1.694
681.481 1.244 1.491 1.530 1.296 1.891 1.133 1.373 1.234 1.464 1.358 1.692
691.482 1.243 1.489 1.532 1.296 1.887 1.132 1.372 1.233 1.463 1.357 1.690
701.483 1.242 1.488 1.533 1.296 1.883 1.130 1.371 1.233 1.462 1.356 1.688
711.484 1.241 1.486 1.534 1.296 1.879 1.129 1.370 1.232 1.461 1.355 1.686
721.485 1.240 1.484 1.536 1.296 1.875 1.127 1.370 1.231 1.460 1.355 1.683
731.485 1.239 1.482 1.537 1.295 1.872 1.126 1.370 1.230 1.460 1.355 1.682
741.486 1.238 1.481 1.539 1.295 1.868 1.124 1.370 1.229 1.459 1.354 1.681
751.486 1.237 1.479 1.540 1.295 1.865 1.122 1.370 1.228 1.458 1.354 1.680
761.486 1.236 1.477 1.542 1.296 1.862 1.120 1.370 1.227 1.457 1.354 1.678
771.487 1.235 1.475 1.543 1.296 1.859 1.118 1.370 1.226 1.456 1.354 1.677
781.487 1.235 1.474 1.546 1.296 1.856 1.116 1.369 1.225 1.455 1.354 1.676
791.488 1.234 1.472 1.548 1.296 1.853 1.114 1.369 1.225 1.454 1.355 1.675
801.488 1.234 1.471 1.550 1.296 1.850 1.112 1.368 1.224 1.454 1.355 1.674
811.489 1.233 1.470 1.553 1.296 1.848 1.110 1.367 1.223 1.453 1.355 1.673
821.489 1.233 1.468 1.556 1.297 1.845 1.109 1.366 1.223 1.453 1.355 1.672
831.490 1.232 1.467 1.559 1.297 1.842 1.107 1.365 1.222 1.453 1.355 1.671
841.490 1.232 1.465 1.563 1.297 1.840 1.105 1.363 1.221 1.453 1.356 1.670
851.490 1.231 1.464 1.566 1.297 1.838 1.103 1.362 1.221 1.453 1.356 1.669
861.490 1.230 1.462 1.570 1.297 1.836 1.102 1.360 1.220 1.453 1.356 1.668
871.491 1.229 1.461 1.574 1.297 1.833 1.100 1.359 1.220 1.453 1.356 1.667
881.492 1.228 1.459 1.577 1.297 1.831 1.098 1.358 1.220 1.453 1.356 1.666
891.494 1.228 1.457 1.581 1.297 1.829 1.096 1.357 1.220 1.453 1.356 1.665
901.495 1.227 1.456 1.584 1.297 1.827 1.094 1.355 1.220 1.453 1.356 1.664
911.496 1.227 1.454 1.587 1.298 1.825 1.092 1.354 1.220 1.453 1.356 1.663
921.498 1.226 1.452 1.591 1.298 1.824 1.090 1.354 1.220 1.453 1.356 1.662
931.500 1.226 1.451 1.595 1.298 1.822 1.088 1.354 1.220 1.453 1.356 1.660
941.502 1.225 1.449 1.597 1.299 1.821 1.086 1.353 1.220 1.453 1.356 1.659
951.503 1.224 1.448 1.600 1.299 1.819 1.084 1.352 1.220 1.453 1.356 1.658
961.505 1.224 1.446 1.604 1.300 1.818 1.082 1.352 1.220 1.453 1.356 1.657
971.506 1.223 1.444 1.608 1.301 1.816 1.079 1.351 1.220 1.453 1.356 1.657
981.508 1.223 1.443 1.611 1.302 1.814 1.077 1.350 1.220 1.453 1.356 1.656
991.509 1.222 1.441 1.614 1.302 1.812 1.075 1.349 1.220 1.453 1.355 1.656
1001.510 1.222 1.440 1.618 1.303 1.810 1.072 1.348 1.220 1.454 1.355 1.655
1011.512 1.222 1.439 1.622 1.304 1.808 1.070 1.347 1.221 1.454 1.355 1.654
1021.513 1.221 1.437 1.626 1.305 1.806 1.068 1.346 1.221 1.454 1.355 1.653
1031.514 1.221 1.436 1.630 1.305 1.804 1.066 1.345 1.221 1.454 1.355 1.652
1041.517 1.221 1.434 1.635 1.306 1.802 1.064 1.344 1.221 1.454 1.355 1.651
1051.519 1.222 1.433 1.639 1.307 1.801 1.062 1.343 1.222 1.454 1.355 1.650
1061.521 1.222 1.431 1.644 1.308 1.799 1.060 1.343 1.222 1.454 1.356 1.649
1071.522 1.222 1.430 1.648 1.308 1.797 1.058 1.342 1.223 1.454 1.356 1.648
1081.523 1.223 1.429 1.652 1.309 1.795 1.055 1.341 1.224 1.454 1.356 1.647
1091.524 1.223 1.427 1.656 1.309 1.794 1.054 1.340 1.224 1.453 1.356 1.645
1101.525 1.224 1.426 1.660 1.309 1.792 1.052 1.339 1.225 1.453 1.356 1.644
1111.527 1.225 1.425 1.663 1.309 1.789 1.050 1.338 1.225 1.453 1.355 1.643
1121.528 1.225 1.424 1.666 1.310 1.787 1.048 1.337 1.226 1.453 1.355 1.642
1131.529 1.226 1.422 1.668 1.311 1.786 1.046 1.335 1.227 1.453 1.355 1.640
1141.531 1.227 1.421 1.671 1.312 1.784 1.045 1.334 1.227 1.453 1.355 1.639
1151.533 1.228 1.420 1.673 1.313 1.782 1.043 1.333 1.228 1.453 1.354 1.638
1161.535 1.229 1.419 1.675 1.314 1.780 1.042 1.332 1.228 1.453 1.354 1.637
1171.537 1.230 1.418 1.678 1.316 1.779 1.040 1.331 1.229 1.453 1.354 1.635
1181.539 1.231 1.416 1.679 1.317 1.777 1.039 1.330 1.229 1.452 1.354 1.634
1191.542 1.232 1.415 1.681 1.319 1.776 1.037 1.329 1.230 1.452 1.354 1.633
1201.544 1.233 1.414 1.682 1.320 1.774 1.036 1.327 1.230 1.452 1.354 1.632
1211.548 1.234 1.413 1.683 1.321 1.773 1.034 1.326 1.231 1.451 1.354 1.630
1221.551 1.235 1.412 1.684 1.323 1.772 1.033 1.325 1.232 1.451 1.354 1.629
1231.555 1.237 1.411 1.685 1.324 1.770 1.032 1.324 1.232 1.451 1.354 1.627
1241.559 1.238 1.410 1.686 1.325 1.769 1.030 1.322 1.233 1.450 1.354 1.626
1251.564 1.239 1.409 1.686 1.326 1.767 1.029 1.321 1.234 1.450 1.353 1.625
1261.569 1.241 1.408 1.687 1.328 1.765 1.028 1.320 1.235 1.450 1.353 1.624
1271.574 1.242 1.407 1.689 1.329 1.764 1.026 1.318 1.235 1.450 1.353 1.623
1281.580 1.244 1.406 1.690 1.331 1.762 1.025 1.317 1.236 1.450 1.353 1.622
1291.585 1.245 1.405 1.692 1.332 1.761 1.024 1.316 1.237 1.449 1.353 1.621
1301.590 1.247 1.404 1.694 1.334 1.760 1.022 1.315 1.238 1.449 1.353 1.620
1311.595 1.248 1.403 1.696 1.335 1.759 1.021 1.314 1.239 1.448 1.353 1.618
1321.600 1.249 1.402 1.699 1.337 1.757 1.019 1.313 1.240 1.448 1.353 1.617
1331.605 1.251 1.401 1.701 1.339 1.756 1.018 1.313 1.241 1.448 1.353 1.615
1341.610 1.252 1.400 1.704 1.341 1.755 1.017 1.312 1.242 1.447 1.353 1.614
1351.614 1.254 1.399 1.707 1.342 1.754 1.015 1.312 1.243 1.447 1.352 1.612
1361.619 1.255 1.398 1.709 1.344 1.753 1.014 1.312 1.244 1.446 1.352 1.611
1371.624 1.256 1.397 1.712 1.346 1.751 1.012 1.312 1.245 1.446 1.352 1.609
1381.628 1.258 1.396 1.714 1.348 1.750 1.011 1.312 1.246 1.445 1.352 1.608
1391.632 1.259 1.395 1.716 1.351 1.749 1.009 1.312 1.247 1.445 1.351 1.607
1401.635 1.261 1.394 1.719 1.353 1.749 1.008 1.312 1.248 1.444 1.351 1.605
1411.639 1.262 1.393 1.721 1.355 1.748 1.006 1.312 1.248 1.444 1.351 1.603
1421.642 1.263 1.391 1.724 1.358 1.747 1.005 1.312 1.249 1.443 1.350 1.602
1431.645 1.264 1.390 1.726 1.360 1.747 1.003 1.312 1.250 1.443 1.350 1.601
1441.648 1.266 1.389 1.729 1.363 1.746 1.002 1.312 1.251 1.442 1.350 1.600
1451.650 1.267 1.387 1.732 1.366 1.745 1.001 1.312 1.251 1.442 1.350 1.599
1461.653 1.268 1.386 1.734 1.368 1.744 1.000 1.312 1.252 1.441 1.350 1.598
1471.655 1.269 1.385 1.737 1.371 1.743 0.999 1.311 1.252 1.440 1.350 1.597
1481.657 1.270 1.383 1.738 1.373 1.742 0.997 1.312 1.253 1.440 1.349 1.595
1491.659 1.271 1.382 1.739 1.376 1.741 0.996 1.312 1.253 1.439 1.349 1.594
1501.660 1.272 1.380 1.741 1.378 1.740 0.995 1.312 1.254 1.438 1.349 1.592
1511.662 1.273 1.379 1.742 1.380 1.739 0.993 1.312 1.254 1.437 1.348 1.591
1521.664 1.274 1.378 1.744 1.382 1.738 0.992 1.313 1.254 1.437 1.348 1.589
1531.665 1.275 1.376 1.745 1.384 1.736 0.991 1.313 1.255 1.436 1.348 1.588
1541.666 1.276 1.375 1.747 1.386 1.735 0.989 1.313 1.255 1.435 1.347 1.586
1551.668 1.277 1.373 1.749 1.388 1.734 0.988 1.314 1.256 1.434 1.347 1.585
1561.669 1.277 1.372 1.751 1.390 1.732 0.987 1.314 1.256 1.434 1.346 1.584
1571.670 1.278 1.371 1.753 1.392 1.731 0.986 1.314 1.257 1.433 1.346 1.582
1581.671 1.279 1.369 1.755 1.394 1.730 0.985 1.314 1.257 1.432 1.346 1.581
1591.672 1.280 1.368 1.756 1.397 1.728 0.984 1.314 1.258 1.432 1.346 1.579
1601.673 1.281 1.367 1.758 1.399 1.726 0.982 1.314 1.258 1.431 1.345 1.578
1611.674 1.282 1.365 1.759 1.401 1.725 0.981 1.314 1.258 1.431 1.345 1.577
1621.675 1.282 1.364 1.760 1.403 1.723 0.980 1.314 1.258 1.430 1.345 1.575
1631.676 1.282 1.362 1.760 1.405 1.722 0.979 1.314 1.259 1.430 1.345 1.574
1641.677 1.283 1.361 1.761 1.407 1.720 0.977 1.314 1.259 1.429 1.345 1.573
1651.678 1.283 1.360 1.762 1.408 1.718 0.976 1.314 1.259 1.428 1.345 1.572
1661.679 1.283 1.358 1.762 1.410 1.717 0.974 1.314 1.259 1.427 1.345 1.570
1671.681 1.284 1.357 1.763 1.411 1.715 0.973 1.314 1.259 1.426 1.345 1.569
1681.683 1.284 1.355 1.764 1.413 1.713 0.971 1.314 1.259 1.425 1.345 1.567
1691.685 1.284 1.354 1.765 1.415 1.712 0.970 1.314 1.259 1.423 1.345 1.566
1701.688 1.284 1.353 1.767 1.416 1.710 0.968 1.314 1.259 1.422 1.345 1.564
1711.690 1.284 1.351 1.768 1.418 1.708 0.967 1.313 1.259 1.420 1.345 1.563
1721.692 1.283 1.350 1.770 1.420 1.707 0.965 1.313 1.259 1.419 1.345 1.561
1731.694 1.283 1.349 1.771 1.421 1.705 0.964 1.313 1.259 1.417 1.345 1.560
1741.697 1.283 1.347 1.772 1.422 1.703 0.963 1.313 1.259 1.416 1.345 1.558
1751.698 1.283 1.346 1.774 1.423 1.701 0.961 1.313 1.259 1.415 1.346 1.557
1761.700 1.283 1.344 1.775 1.425 1.699 0.960 1.313 1.259 1.414 1.346 1.555
1771.702 1.284 1.343 1.776 1.426 1.697 0.959 1.313 1.259 1.413 1.346 1.554
1781.704 1.284 1.341 1.777 1.427 1.695 0.958 1.314 1.260 1.412 1.346 1.553
1791.706 1.284 1.340 1.777 1.429 1.693 0.957 1.314 1.260 1.411 1.346 1.552
1801.708 1.285 1.338 1.778 1.430 1.691 0.956 1.314 1.260 1.409 1.346 1.551
1811.711 1.285 1.337 1.779 1.431 1.688 0.955 1.314 1.260 1.408 1.346 1.550
1821.712 1.286 1.335 1.780 1.433 1.686 0.954 1.314 1.260 1.407 1.346 1.549
1831.714 1.287 1.334 1.781 1.434 1.684 0.952 1.314 1.259 1.405 1.347 1.548
1841.716 1.287 1.333 1.782 1.435 1.682 0.951 1.314 1.259 1.404 1.347 1.547
1851.718 1.288 1.331 1.782 1.437 1.680 0.950 1.315 1.259 1.402 1.347 1.546
1861.720 1.288 1.330 1.782 1.438 1.678 0.949 1.315 1.259 1.401 1.347 1.545
1871.721 1.289 1.329 1.782 1.439 1.676 0.948 1.315 1.259 1.399 1.348 1.544
1881.724 1.290 1.327 1.782 1.440 1.674 0.948 1.315 1.258 1.398 1.348 1.543
1891.725 1.290 1.326 1.781 1.440 1.672 0.947 1.315 1.258 1.396 1.348 1.542
1901.727 1.291 1.325 1.780 1.441 1.670 0.946 1.314 1.257 1.395 1.348 1.541
1911.729 1.291 1.323 1.779 1.441 1.668 0.945 1.314 1.257 1.393 1.348 1.540
1921.731 1.292 1.322 1.778 1.442 1.666 0.944 1.314 1.256 1.391 1.348 1.539
1931.732 1.292 1.321 1.777 1.443 1.664 0.943 1.314 1.256 1.390 1.348 1.538
1941.734 1.292 1.319 1.776 1.444 1.663 0.942 1.313 1.255 1.389 1.348 1.537
1951.737 1.293 1.318 1.775 1.444 1.661 0.941 1.313 1.255 1.387 1.348 1.536
1961.739 1.293 1.317 1.774 1.445 1.659 0.941 1.312 1.254 1.386 1.348 1.535
1971.741 1.293 1.315 1.773 1.445 1.657 0.940 1.311 1.254 1.385 1.348 1.534
1981.742 1.293 1.314 1.772 1.446 1.655 0.939 1.311 1.253 1.383 1.348 1.533
1991.743 1.294 1.313 1.771 1.446 1.653 0.938 1.310 1.252 1.382 1.348 1.531
2001.745 1.294 1.312 1.770 1.447 1.651 0.937 1.309 1.252 1.381 1.348 1.530
2011.747 1.294 1.311 1.769 1.447 1.650 0.936 1.308 1.251 1.379 1.348 1.529
2021.749 1.294 1.309 1.768 1.448 1.648 0.936 1.307 1.250 1.378 1.348 1.528
2031.751 1.294 1.308 1.767 1.448 1.646 0.935 1.306 1.250 1.377 1.349 1.526
2041.752 1.294 1.307 1.765 1.448 1.644 0.934 1.305 1.249 1.375 1.349 1.525
2051.754 1.294 1.306 1.764 1.449 1.642 0.934 1.305 1.248 1.374 1.349 1.524
2061.756 1.294 1.305 1.762 1.449 1.640 0.933 1.304 1.247 1.373 1.349 1.523
2071.758 1.294 1.304 1.761 1.449 1.639 0.932 1.303 1.247 1.372 1.350 1.521
2081.760 1.293 1.303 1.759 1.449 1.637 0.932 1.302 1.246 1.370 1.350 1.520
2091.762 1.293 1.301 1.758 1.450 1.635 0.931 1.302 1.245 1.369 1.350 1.519
2101.764 1.292 1.300 1.756 1.450 1.633 0.930 1.301 1.244 1.367 1.351 1.518
2111.766 1.292 1.299 1.754 1.450 1.631 0.930 1.300 1.244 1.366 1.351 1.517
2121.768 1.291 1.298 1.752 1.451 1.629 0.929 1.300 1.243 1.364 1.351 1.516
2131.769 1.290 1.297 1.751 1.451 1.627 0.928 1.299 1.242 1.363 1.351 1.514
2141.771 1.289 1.295 1.750 1.451 1.626 0.928 1.299 1.241 1.361 1.352 1.514
2151.772 1.289 1.294 1.748 1.451 1.624 0.927 1.298 1.241 1.360 1.352 1.513
2161.774 1.288 1.293 1.747 1.451 1.622 0.927 1.298 1.240 1.359 1.352 1.512
2171.776 1.287 1.292 1.746 1.451 1.620 0.926 1.298 1.239 1.357 1.352 1.511
2181.777 1.287 1.291 1.744 1.451 1.618 0.925 1.298 1.239 1.356 1.353 1.510
2191.777 1.286 1.290 1.743 1.451 1.616 0.925 1.297 1.238 1.355 1.353 1.509
2201.778 1.285 1.289 1.742 1.451 1.614 0.924 1.297 1.237 1.353 1.353 1.508
2211.779 1.285 1.288 1.741 1.451 1.612 0.923 1.297 1.237 1.352 1.353 1.507
2221.781 1.284 1.287 1.740 1.451 1.610 0.923 1.296 1.236 1.351 1.353 1.505
2231.782 1.284 1.286 1.739 1.451 1.608 0.922 1.296 1.236 1.349 1.354 1.504
2241.784 1.283 1.285 1.738 1.451 1.606 0.922 1.296 1.235 1.348 1.354 1.504
2251.786 1.282 1.284 1.738 1.451 1.604 0.921 1.295 1.235 1.347 1.354 1.503
2261.787 1.282 1.283 1.737 1.451 1.602 0.920 1.295 1.234 1.346 1.355 1.502
2271.788 1.281 1.282 1.737 1.451 1.600 0.920 1.295 1.234 1.344 1.355 1.501
2281.790 1.281 1.282 1.736 1.451 1.598 0.919 1.294 1.233 1.343 1.355 1.500
2291.791 1.280 1.281 1.735 1.450 1.596 0.919 1.294 1.233 1.342 1.356 1.500
2301.793 1.280 1.280 1.734 1.450 1.594 0.918 1.294 1.232 1.341 1.356 1.499
2311.795 1.279 1.279 1.733 1.449 1.592 0.918 1.294 1.232 1.339 1.356 1.498
2321.797 1.279 1.279 1.732 1.449 1.590 0.917 1.293 1.231 1.338 1.356 1.497
2331.798 1.278 1.278 1.731 1.448 1.588 0.917 1.293 1.230 1.337 1.356 1.497
2341.800 1.278 1.277 1.730 1.448 1.585 0.916 1.292 1.230 1.336 1.356 1.496
2351.801 1.278 1.277 1.728 1.447 1.583 0.916 1.292 1.229 1.335 1.356 1.495
2361.802 1.277 1.276 1.727 1.447 1.581 0.915 1.291 1.228 1.334 1.356 1.494
2371.803 1.277 1.275 1.726 1.446 1.579 0.915 1.291 1.228 1.333 1.356 1.494
2381.803 1.277 1.275 1.725 1.446 1.577 0.914 1.290 1.227 1.332 1.356 1.493
2391.804 1.277 1.274 1.723 1.445 1.575 0.914 1.290 1.226 1.331 1.356 1.492
2401.803 1.276 1.274 1.722 1.444 1.573 0.914 1.289 1.226 1.329 1.356 1.491
2411.802 1.276 1.273 1.721 1.443 1.571 0.913 1.289 1.225 1.328 1.355 1.490
2421.801 1.276 1.272 1.720 1.443 1.569 0.913 1.288 1.225 1.327 1.355 1.490
2431.800 1.276 1.272 1.718 1.442 1.567 0.913 1.287 1.224 1.326 1.355 1.489
2441.799 1.276 1.271 1.717 1.441 1.565 0.912 1.286 1.224 1.325 1.355 1.488
2451.798 1.276 1.271 1.716 1.441 1.564 0.912 1.286 1.223 1.324 1.355 1.487
2461.797 1.276 1.270 1.715 1.440 1.562 0.912 1.285 1.223 1.324 1.355 1.487
2471.796 1.276 1.270 1.714 1.439 1.560 0.911 1.284 1.223 1.323 1.355 1.486
2481.794 1.276 1.269 1.713 1.439 1.558 0.911 1.283 1.222 1.322 1.355 1.485
2491.791 1.276 1.268 1.712 1.438 1.556 0.911 1.282 1.222 1.321 1.355 1.485
2501.791 1.276 1.268 1.712 1.438 1.556 0.911 1.282 1.222 1.321 1.355 1.485
Data for figure immediately follows

Data for Appendix 4 - Long Memory Hypothesis Tests: Equity (Malaysia - Turkey)

xiMalaysiaPhilippinesRussiaSingaporeTaiwanThailandIsraelKuwaitNigeriaSaudi ArabiaSouth AfricaTurkey
01.624 1.439 1.770 1.622 1.605 1.896 0.982 1.841 1.446 2.205 1.550 1.557
11.575 1.409 1.727 1.595 1.577 1.852 0.981 1.840 1.326 2.203 1.492 1.507
21.538 1.396 1.704 1.569 1.541 1.825 0.987 1.835 1.275 2.203 1.454 1.485
31.522 1.383 1.688 1.543 1.518 1.805 0.990 1.834 1.253 2.185 1.438 1.478
41.508 1.381 1.676 1.525 1.501 1.794 1.003 1.814 1.250 2.178 1.432 1.468
51.503 1.383 1.661 1.511 1.491 1.793 1.017 1.811 1.251 2.172 1.432 1.466
61.499 1.382 1.648 1.498 1.483 1.796 1.028 1.806 1.250 2.168 1.431 1.469
71.498 1.374 1.639 1.486 1.472 1.795 1.034 1.800 1.247 2.151 1.433 1.471
81.495 1.366 1.632 1.475 1.462 1.792 1.036 1.792 1.241 2.129 1.430 1.471
91.493 1.359 1.622 1.466 1.450 1.786 1.033 1.783 1.234 2.123 1.426 1.469
101.492 1.353 1.612 1.456 1.437 1.780 1.029 1.774 1.227 2.109 1.423 1.463
111.490 1.344 1.602 1.446 1.422 1.775 1.027 1.766 1.220 2.087 1.420 1.458
121.488 1.332 1.591 1.436 1.408 1.764 1.027 1.760 1.215 2.069 1.420 1.452
131.487 1.319 1.581 1.426 1.395 1.754 1.026 1.753 1.210 2.049 1.417 1.446
141.483 1.306 1.571 1.417 1.382 1.743 1.025 1.735 1.206 2.029 1.413 1.440
151.480 1.295 1.563 1.408 1.371 1.733 1.024 1.717 1.202 2.014 1.407 1.435
161.477 1.284 1.557 1.401 1.364 1.724 1.023 1.700 1.198 2.002 1.402 1.430
171.474 1.273 1.554 1.394 1.357 1.716 1.024 1.686 1.195 1.994 1.399 1.428
181.471 1.265 1.551 1.387 1.351 1.709 1.024 1.672 1.193 1.987 1.396 1.426
191.468 1.258 1.549 1.381 1.346 1.703 1.024 1.660 1.190 1.977 1.394 1.425
201.465 1.251 1.547 1.376 1.340 1.698 1.024 1.649 1.188 1.968 1.392 1.424
211.462 1.246 1.544 1.371 1.335 1.693 1.024 1.639 1.186 1.962 1.392 1.422
221.458 1.241 1.539 1.366 1.331 1.689 1.025 1.631 1.184 1.960 1.393 1.419
231.454 1.236 1.535 1.361 1.327 1.684 1.026 1.625 1.182 1.959 1.394 1.419
241.450 1.231 1.529 1.356 1.323 1.680 1.026 1.620 1.180 1.958 1.393 1.417
251.445 1.226 1.524 1.352 1.320 1.678 1.027 1.616 1.178 1.956 1.390 1.414
261.442 1.222 1.519 1.347 1.316 1.677 1.027 1.613 1.177 1.954 1.387 1.413
271.438 1.219 1.515 1.342 1.313 1.678 1.027 1.610 1.175 1.951 1.383 1.412
281.434 1.216 1.512 1.337 1.310 1.677 1.028 1.608 1.174 1.947 1.380 1.412
291.430 1.212 1.508 1.332 1.308 1.675 1.028 1.604 1.173 1.944 1.377 1.411
301.427 1.208 1.504 1.327 1.306 1.672 1.027 1.600 1.172 1.942 1.374 1.412
311.425 1.205 1.501 1.323 1.304 1.670 1.026 1.597 1.171 1.940 1.372 1.412
321.422 1.202 1.498 1.319 1.303 1.668 1.026 1.594 1.170 1.938 1.370 1.414
331.420 1.200 1.495 1.315 1.301 1.667 1.026 1.590 1.169 1.935 1.368 1.414
341.416 1.198 1.493 1.311 1.299 1.665 1.026 1.586 1.168 1.934 1.367 1.414
351.413 1.197 1.491 1.307 1.297 1.665 1.028 1.582 1.166 1.935 1.367 1.415
361.410 1.196 1.489 1.303 1.295 1.664 1.029 1.579 1.164 1.936 1.369 1.417
371.407 1.194 1.486 1.299 1.294 1.664 1.030 1.575 1.163 1.937 1.371 1.418
381.404 1.192 1.484 1.295 1.292 1.664 1.032 1.572 1.162 1.938 1.373 1.420
391.401 1.190 1.483 1.291 1.291 1.664 1.034 1.569 1.160 1.936 1.374 1.423
401.399 1.188 1.482 1.288 1.289 1.665 1.035 1.566 1.158 1.933 1.375 1.424
411.396 1.186 1.482 1.284 1.287 1.666 1.036 1.564 1.156 1.929 1.376 1.426
421.394 1.184 1.481 1.281 1.286 1.666 1.037 1.561 1.153 1.926 1.376 1.427
431.391 1.182 1.479 1.278 1.285 1.666 1.038 1.559 1.151 1.924 1.377 1.429
441.388 1.181 1.477 1.275 1.283 1.667 1.040 1.556 1.149 1.921 1.376 1.429
451.385 1.179 1.476 1.272 1.281 1.667 1.041 1.552 1.147 1.918 1.376 1.429
461.382 1.178 1.475 1.270 1.279 1.668 1.043 1.549 1.145 1.916 1.376 1.429
471.379 1.177 1.475 1.267 1.278 1.670 1.044 1.546 1.142 1.913 1.376 1.429
481.376 1.176 1.474 1.265 1.276 1.671 1.046 1.543 1.140 1.909 1.376 1.430
491.373 1.176 1.473 1.262 1.275 1.672 1.048 1.539 1.138 1.904 1.377 1.431
501.370 1.175 1.471 1.260 1.274 1.672 1.051 1.535 1.136 1.899 1.377 1.432
511.367 1.174 1.469 1.258 1.274 1.672 1.053 1.531 1.135 1.894 1.377 1.434
521.365 1.173 1.468 1.255 1.273 1.672 1.055 1.528 1.133 1.889 1.377 1.435
531.362 1.172 1.467 1.253 1.272 1.672 1.057 1.524 1.132 1.883 1.377 1.436
541.360 1.171 1.466 1.251 1.271 1.671 1.058 1.521 1.131 1.877 1.377 1.438
551.358 1.170 1.465 1.249 1.270 1.671 1.060 1.518 1.129 1.871 1.376 1.438
561.356 1.169 1.463 1.247 1.269 1.672 1.061 1.515 1.128 1.866 1.375 1.439
571.354 1.169 1.462 1.246 1.268 1.672 1.063 1.513 1.127 1.861 1.374 1.440
581.352 1.169 1.461 1.244 1.266 1.673 1.064 1.511 1.125 1.856 1.373 1.441
591.350 1.168 1.460 1.243 1.265 1.674 1.066 1.509 1.125 1.851 1.372 1.441
601.348 1.168 1.458 1.242 1.264 1.674 1.067 1.506 1.124 1.847 1.372 1.442
611.346 1.167 1.457 1.240 1.263 1.675 1.067 1.504 1.124 1.842 1.372 1.442
621.345 1.167 1.456 1.239 1.261 1.675 1.068 1.502 1.123 1.837 1.373 1.442
631.343 1.167 1.454 1.238 1.260 1.675 1.068 1.500 1.123 1.833 1.374 1.443
641.342 1.166 1.452 1.237 1.259 1.675 1.069 1.498 1.123 1.828 1.374 1.444
651.341 1.166 1.451 1.236 1.258 1.674 1.070 1.497 1.123 1.824 1.374 1.444
661.340 1.165 1.449 1.235 1.257 1.673 1.071 1.495 1.123 1.819 1.374 1.444
671.339 1.165 1.448 1.234 1.256 1.672 1.072 1.494 1.122 1.815 1.373 1.443
681.338 1.164 1.446 1.233 1.255 1.672 1.072 1.492 1.122 1.810 1.372 1.443
691.338 1.164 1.445 1.232 1.254 1.671 1.072 1.489 1.121 1.806 1.372 1.442
701.338 1.164 1.444 1.231 1.253 1.670 1.072 1.487 1.121 1.802 1.371 1.441
711.337 1.163 1.444 1.231 1.252 1.669 1.072 1.485 1.121 1.798 1.369 1.441
721.337 1.163 1.443 1.230 1.251 1.668 1.071 1.484 1.120 1.795 1.368 1.441
731.336 1.163 1.442 1.230 1.250 1.667 1.071 1.482 1.120 1.791 1.367 1.441
741.336 1.163 1.441 1.230 1.250 1.667 1.071 1.480 1.120 1.789 1.367 1.441
751.335 1.163 1.441 1.229 1.249 1.667 1.071 1.478 1.119 1.787 1.366 1.441
761.335 1.163 1.441 1.229 1.248 1.668 1.072 1.476 1.119 1.785 1.366 1.441
771.334 1.163 1.441 1.229 1.247 1.668 1.072 1.475 1.119 1.783 1.366 1.441
781.333 1.162 1.441 1.229 1.246 1.668 1.073 1.473 1.119 1.781 1.366 1.441
791.332 1.162 1.440 1.229 1.245 1.667 1.074 1.472 1.119 1.778 1.366 1.441
801.332 1.161 1.439 1.228 1.244 1.667 1.075 1.471 1.118 1.776 1.366 1.440
811.331 1.161 1.438 1.228 1.243 1.667 1.076 1.470 1.118 1.773 1.367 1.439
821.330 1.161 1.437 1.228 1.242 1.667 1.077 1.469 1.117 1.770 1.367 1.439
831.329 1.160 1.436 1.228 1.240 1.668 1.079 1.468 1.117 1.767 1.367 1.439
841.329 1.160 1.435 1.227 1.239 1.668 1.081 1.467 1.116 1.765 1.366 1.439
851.329 1.160 1.434 1.227 1.239 1.669 1.082 1.466 1.115 1.763 1.367 1.439
861.328 1.160 1.432 1.227 1.238 1.670 1.084 1.465 1.114 1.760 1.367 1.439
871.328 1.160 1.430 1.227 1.237 1.671 1.085 1.464 1.113 1.758 1.368 1.439
881.328 1.161 1.429 1.227 1.237 1.673 1.087 1.463 1.112 1.756 1.368 1.439
891.328 1.161 1.427 1.227 1.236 1.674 1.088 1.462 1.111 1.754 1.369 1.438
901.328 1.161 1.426 1.227 1.236 1.675 1.091 1.461 1.110 1.751 1.369 1.438
911.328 1.161 1.424 1.227 1.235 1.676 1.093 1.459 1.109 1.748 1.370 1.438
921.328 1.162 1.422 1.227 1.234 1.678 1.096 1.458 1.109 1.745 1.371 1.439
931.328 1.162 1.420 1.227 1.234 1.679 1.099 1.458 1.108 1.743 1.373 1.439
941.327 1.163 1.418 1.227 1.233 1.681 1.102 1.457 1.107 1.739 1.374 1.440
951.327 1.163 1.416 1.227 1.232 1.683 1.104 1.456 1.107 1.736 1.376 1.441
961.326 1.164 1.414 1.227 1.232 1.686 1.107 1.455 1.107 1.733 1.379 1.442
971.326 1.164 1.411 1.227 1.231 1.688 1.109 1.454 1.106 1.730 1.381 1.442
981.325 1.165 1.409 1.227 1.231 1.690 1.112 1.453 1.106 1.727 1.383 1.443
991.325 1.165 1.407 1.227 1.230 1.692 1.114 1.451 1.106 1.723 1.386 1.444
1001.325 1.166 1.405 1.227 1.230 1.694 1.116 1.450 1.105 1.719 1.389 1.444
1011.324 1.167 1.403 1.227 1.229 1.697 1.118 1.449 1.105 1.716 1.392 1.445
1021.324 1.168 1.401 1.227 1.229 1.699 1.121 1.448 1.105 1.713 1.394 1.445
1031.324 1.169 1.400 1.227 1.228 1.702 1.123 1.446 1.104 1.710 1.397 1.445
1041.324 1.169 1.398 1.227 1.228 1.705 1.125 1.445 1.104 1.706 1.401 1.445
1051.324 1.170 1.397 1.227 1.227 1.708 1.126 1.443 1.104 1.703 1.404 1.446
1061.324 1.171 1.396 1.227 1.227 1.711 1.129 1.442 1.104 1.699 1.407 1.446
1071.324 1.172 1.395 1.227 1.227 1.715 1.130 1.441 1.104 1.696 1.410 1.446
1081.324 1.173 1.394 1.227 1.227 1.718 1.132 1.440 1.104 1.693 1.413 1.447
1091.324 1.174 1.392 1.228 1.226 1.722 1.134 1.438 1.104 1.690 1.416 1.448
1101.324 1.174 1.391 1.227 1.226 1.725 1.135 1.437 1.104 1.687 1.419 1.449
1111.324 1.175 1.390 1.227 1.226 1.728 1.137 1.436 1.104 1.684 1.422 1.450
1121.324 1.176 1.389 1.227 1.225 1.731 1.138 1.435 1.104 1.681 1.425 1.451
1131.324 1.176 1.387 1.227 1.225 1.734 1.139 1.433 1.103 1.678 1.428 1.452
1141.324 1.177 1.386 1.227 1.225 1.736 1.140 1.432 1.103 1.675 1.430 1.453
1151.324 1.177 1.385 1.227 1.224 1.739 1.141 1.431 1.102 1.672 1.433 1.455
1161.324 1.178 1.383 1.227 1.224 1.741 1.142 1.430 1.101 1.670 1.436 1.457
1171.324 1.178 1.382 1.226 1.224 1.744 1.144 1.429 1.101 1.667 1.439 1.458
1181.324 1.179 1.381 1.226 1.224 1.747 1.145 1.427 1.100 1.665 1.442 1.460
1191.323 1.180 1.379 1.226 1.224 1.749 1.147 1.426 1.100 1.662 1.445 1.462
1201.323 1.180 1.378 1.226 1.223 1.752 1.149 1.426 1.099 1.660 1.447 1.463
1211.323 1.181 1.378 1.226 1.223 1.754 1.150 1.425 1.098 1.657 1.450 1.464
1221.323 1.182 1.377 1.226 1.223 1.756 1.152 1.424 1.097 1.655 1.453 1.466
1231.322 1.182 1.376 1.226 1.223 1.759 1.153 1.423 1.096 1.652 1.456 1.467
1241.322 1.183 1.375 1.226 1.223 1.761 1.155 1.423 1.095 1.650 1.458 1.469
1251.322 1.183 1.374 1.226 1.222 1.763 1.157 1.423 1.094 1.648 1.460 1.470
1261.322 1.184 1.374 1.226 1.222 1.766 1.159 1.423 1.093 1.645 1.462 1.472
1271.322 1.185 1.373 1.226 1.222 1.768 1.160 1.423 1.093 1.643 1.464 1.474
1281.322 1.185 1.373 1.226 1.222 1.771 1.162 1.422 1.092 1.641 1.465 1.475
1291.322 1.186 1.372 1.226 1.222 1.773 1.163 1.422 1.090 1.638 1.467 1.477
1301.321 1.186 1.371 1.226 1.222 1.776 1.164 1.421 1.089 1.636 1.469 1.478
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1331.321 1.188 1.370 1.226 1.221 1.784 1.165 1.420 1.085 1.629 1.473 1.483
1341.321 1.188 1.370 1.226 1.221 1.787 1.166 1.420 1.084 1.626 1.475 1.485
1351.321 1.189 1.370 1.226 1.221 1.790 1.168 1.419 1.083 1.624 1.477 1.486
1361.321 1.189 1.370 1.226 1.221 1.793 1.169 1.419 1.082 1.622 1.478 1.488
1371.322 1.189 1.370 1.226 1.222 1.796 1.170 1.419 1.081 1.619 1.480 1.489
1381.322 1.190 1.369 1.226 1.222 1.798 1.172 1.419 1.080 1.617 1.482 1.491
1391.322 1.190 1.369 1.227 1.222 1.801 1.173 1.418 1.079 1.615 1.484 1.492
1401.322 1.191 1.369 1.227 1.222 1.803 1.174 1.418 1.078 1.612 1.486 1.494
1411.322 1.191 1.368 1.227 1.222 1.806 1.175 1.418 1.077 1.610 1.487 1.496
1421.322 1.192 1.368 1.227 1.222 1.808 1.176 1.418 1.076 1.608 1.489 1.498
1431.322 1.193 1.367 1.228 1.222 1.809 1.177 1.418 1.075 1.605 1.490 1.499
1441.322 1.193 1.367 1.228 1.222 1.811 1.178 1.418 1.074 1.603 1.492 1.501
1451.322 1.194 1.366 1.228 1.222 1.813 1.180 1.418 1.073 1.601 1.495 1.502
1461.322 1.194 1.366 1.228 1.222 1.815 1.181 1.418 1.073 1.599 1.497 1.503
1471.322 1.195 1.366 1.229 1.222 1.817 1.183 1.418 1.072 1.597 1.499 1.505
1481.322 1.195 1.366 1.229 1.222 1.819 1.184 1.418 1.071 1.594 1.502 1.506
1491.322 1.196 1.366 1.229 1.222 1.821 1.186 1.418 1.071 1.592 1.504 1.508
1501.322 1.196 1.365 1.229 1.222 1.822 1.187 1.419 1.070 1.590 1.507 1.509
1511.321 1.197 1.365 1.230 1.222 1.824 1.189 1.419 1.070 1.588 1.509 1.510
1521.321 1.197 1.365 1.230 1.222 1.825 1.191 1.420 1.069 1.586 1.511 1.511
1531.320 1.198 1.364 1.230 1.222 1.826 1.194 1.420 1.069 1.584 1.513 1.512
1541.320 1.199 1.364 1.231 1.222 1.827 1.196 1.421 1.068 1.582 1.515 1.513
1551.320 1.199 1.364 1.231 1.222 1.829 1.198 1.421 1.067 1.580 1.516 1.513
1561.319 1.200 1.363 1.231 1.222 1.830 1.201 1.422 1.066 1.578 1.518 1.514
1571.319 1.201 1.363 1.231 1.222 1.832 1.203 1.422 1.065 1.576 1.520 1.515
1581.318 1.202 1.362 1.231 1.222 1.833 1.205 1.423 1.065 1.575 1.522 1.515
1591.318 1.203 1.361 1.232 1.222 1.834 1.207 1.423 1.064 1.573 1.524 1.516
1601.318 1.204 1.361 1.232 1.222 1.835 1.210 1.423 1.063 1.571 1.526 1.517
1611.317 1.205 1.360 1.232 1.222 1.835 1.211 1.423 1.062 1.569 1.528 1.517
1621.317 1.205 1.359 1.232 1.223 1.836 1.213 1.423 1.061 1.567 1.530 1.518
1631.316 1.206 1.359 1.232 1.223 1.837 1.215 1.423 1.060 1.566 1.532 1.518
1641.316 1.207 1.358 1.233 1.223 1.837 1.216 1.423 1.059 1.564 1.533 1.519
1651.315 1.208 1.357 1.233 1.223 1.837 1.218 1.423 1.058 1.562 1.535 1.519
1661.314 1.209 1.357 1.233 1.223 1.837 1.220 1.423 1.058 1.560 1.536 1.519
1671.313 1.210 1.356 1.233 1.224 1.838 1.221 1.423 1.057 1.558 1.537 1.519
1681.312 1.210 1.355 1.233 1.224 1.838 1.223 1.423 1.056 1.556 1.539 1.519
1691.311 1.211 1.355 1.233 1.224 1.838 1.224 1.423 1.055 1.554 1.539 1.520
1701.310 1.212 1.354 1.233 1.225 1.839 1.224 1.424 1.054 1.552 1.540 1.520
1711.310 1.213 1.353 1.233 1.225 1.839 1.225 1.424 1.053 1.550 1.542 1.520
1721.309 1.214 1.352 1.233 1.226 1.839 1.225 1.425 1.053 1.548 1.542 1.520
1731.308 1.215 1.351 1.233 1.226 1.839 1.226 1.425 1.052 1.546 1.543 1.520
1741.308 1.215 1.350 1.233 1.227 1.839 1.226 1.425 1.051 1.544 1.544 1.521
1751.307 1.216 1.349 1.233 1.227 1.839 1.227 1.425 1.051 1.542 1.546 1.521
1761.306 1.217 1.348 1.233 1.228 1.839 1.227 1.425 1.050 1.540 1.547 1.521
1771.306 1.217 1.347 1.234 1.228 1.839 1.227 1.425 1.049 1.538 1.548 1.522
1781.305 1.218 1.346 1.234 1.229 1.839 1.228 1.426 1.049 1.536 1.549 1.522
1791.305 1.219 1.345 1.234 1.229 1.839 1.228 1.426 1.048 1.534 1.550 1.523
1801.304 1.219 1.344 1.234 1.229 1.839 1.228 1.426 1.047 1.532 1.552 1.523
1811.304 1.220 1.343 1.235 1.230 1.838 1.229 1.426 1.047 1.530 1.553 1.524
1821.303 1.220 1.343 1.235 1.230 1.838 1.229 1.426 1.046 1.528 1.555 1.525
1831.302 1.220 1.342 1.235 1.231 1.838 1.229 1.426 1.046 1.525 1.557 1.525
1841.302 1.221 1.341 1.235 1.231 1.837 1.229 1.427 1.045 1.523 1.558 1.526
1851.301 1.221 1.340 1.236 1.231 1.837 1.229 1.427 1.045 1.521 1.559 1.526
1861.300 1.222 1.339 1.236 1.232 1.837 1.228 1.427 1.045 1.519 1.560 1.527
1871.299 1.222 1.339 1.236 1.232 1.836 1.228 1.428 1.044 1.517 1.561 1.527
1881.299 1.222 1.338 1.237 1.233 1.836 1.229 1.428 1.044 1.515 1.562 1.528
1891.298 1.223 1.338 1.237 1.233 1.836 1.229 1.429 1.043 1.513 1.563 1.528
1901.298 1.223 1.337 1.237 1.233 1.836 1.229 1.429 1.043 1.511 1.564 1.528
1911.297 1.224 1.337 1.237 1.234 1.835 1.229 1.429 1.043 1.509 1.565 1.528
1921.296 1.224 1.336 1.238 1.234 1.835 1.229 1.429 1.042 1.507 1.565 1.529
1931.296 1.224 1.336 1.238 1.234 1.834 1.229 1.430 1.042 1.505 1.566 1.529
1941.295 1.225 1.336 1.238 1.235 1.833 1.229 1.430 1.041 1.503 1.565 1.529
1951.294 1.225 1.335 1.238 1.235 1.832 1.230 1.430 1.041 1.501 1.565 1.530
1961.294 1.226 1.335 1.239 1.235 1.832 1.230 1.430 1.040 1.499 1.565 1.530
1971.293 1.226 1.335 1.239 1.236 1.831 1.230 1.430 1.040 1.497 1.565 1.531
1981.293 1.226 1.335 1.239 1.236 1.831 1.230 1.430 1.039 1.495 1.564 1.531
1991.292 1.227 1.335 1.239 1.236 1.830 1.230 1.431 1.039 1.493 1.564 1.532
2001.291 1.227 1.334 1.240 1.236 1.830 1.230 1.431 1.038 1.491 1.564 1.532
2011.291 1.228 1.334 1.240 1.236 1.829 1.230 1.432 1.038 1.490 1.564 1.533
2021.290 1.228 1.334 1.240 1.236 1.829 1.230 1.433 1.037 1.488 1.564 1.533
2031.289 1.229 1.334 1.241 1.237 1.828 1.230 1.434 1.037 1.486 1.564 1.534
2041.289 1.229 1.334 1.241 1.237 1.828 1.231 1.434 1.037 1.484 1.563 1.534
2051.288 1.230 1.333 1.241 1.237 1.827 1.232 1.435 1.036 1.482 1.563 1.535
2061.288 1.230 1.333 1.242 1.237 1.826 1.232 1.435 1.036 1.481 1.562 1.535
2071.288 1.230 1.332 1.242 1.237 1.825 1.233 1.435 1.035 1.479 1.562 1.535
2081.287 1.230 1.332 1.242 1.237 1.825 1.234 1.436 1.035 1.477 1.561 1.535
2091.287 1.231 1.332 1.243 1.237 1.823 1.234 1.436 1.034 1.476 1.561 1.535
2101.286 1.231 1.331 1.243 1.237 1.822 1.235 1.436 1.034 1.474 1.560 1.535
2111.285 1.231 1.331 1.243 1.237 1.821 1.235 1.436 1.034 1.473 1.560 1.534
2121.285 1.232 1.330 1.244 1.237 1.820 1.235 1.436 1.033 1.471 1.560 1.534
2131.284 1.232 1.330 1.244 1.237 1.819 1.236 1.436 1.032 1.470 1.560 1.534
2141.284 1.232 1.330 1.244 1.237 1.817 1.237 1.436 1.032 1.469 1.560 1.534
2151.283 1.233 1.330 1.245 1.237 1.816 1.237 1.437 1.031 1.467 1.559 1.534
2161.283 1.233 1.330 1.245 1.237 1.815 1.238 1.437 1.030 1.466 1.559 1.533
2171.282 1.234 1.330 1.245 1.237 1.814 1.239 1.437 1.030 1.464 1.558 1.533
2181.282 1.234 1.329 1.246 1.236 1.813 1.240 1.437 1.029 1.463 1.557 1.533
2191.281 1.235 1.329 1.246 1.236 1.811 1.241 1.437 1.029 1.462 1.557 1.533
2201.281 1.235 1.329 1.246 1.236 1.810 1.241 1.437 1.028 1.460 1.556 1.532
2211.280 1.235 1.328 1.246 1.236 1.809 1.242 1.437 1.027 1.459 1.556 1.531
2221.280 1.236 1.328 1.247 1.235 1.808 1.243 1.438 1.027 1.458 1.555 1.531
2231.279 1.236 1.328 1.247 1.235 1.806 1.244 1.438 1.026 1.457 1.555 1.530
2241.278 1.237 1.327 1.247 1.235 1.805 1.245 1.438 1.025 1.455 1.555 1.530
2251.278 1.237 1.327 1.247 1.235 1.804 1.245 1.438 1.025 1.454 1.555 1.529
2261.277 1.238 1.326 1.247 1.234 1.803 1.246 1.438 1.024 1.453 1.555 1.529
2271.276 1.239 1.326 1.247 1.234 1.802 1.246 1.438 1.024 1.451 1.554 1.528
2281.276 1.239 1.325 1.247 1.234 1.801 1.247 1.438 1.023 1.450 1.554 1.528
2291.275 1.240 1.325 1.248 1.234 1.799 1.247 1.438 1.022 1.449 1.554 1.528
2301.275 1.240 1.325 1.248 1.233 1.798 1.247 1.438 1.022 1.447 1.554 1.527
2311.274 1.241 1.324 1.248 1.233 1.797 1.247 1.438 1.021 1.446 1.554 1.527
2321.274 1.241 1.324 1.249 1.233 1.796 1.248 1.438 1.020 1.445 1.553 1.526
2331.273 1.242 1.323 1.249 1.233 1.795 1.248 1.438 1.020 1.444 1.553 1.525
2341.273 1.242 1.323 1.249 1.232 1.794 1.248 1.437 1.019 1.442 1.553 1.525
2351.272 1.243 1.323 1.249 1.232 1.793 1.249 1.437 1.019 1.441 1.552 1.524
2361.272 1.243 1.322 1.250 1.232 1.792 1.249 1.437 1.018 1.440 1.552 1.523
2371.272 1.244 1.322 1.250 1.232 1.791 1.249 1.437 1.017 1.438 1.552 1.523
2381.271 1.244 1.322 1.250 1.232 1.790 1.248 1.437 1.017 1.437 1.552 1.522
2391.271 1.245 1.321 1.250 1.232 1.790 1.248 1.437 1.016 1.436 1.551 1.522
2401.271 1.245 1.321 1.250 1.232 1.789 1.248 1.437 1.015 1.435 1.551 1.521
2411.270 1.246 1.321 1.250 1.231 1.788 1.248 1.437 1.015 1.435 1.551 1.521
2421.270 1.247 1.321 1.250 1.231 1.787 1.247 1.438 1.014 1.434 1.550 1.520
2431.270 1.247 1.321 1.250 1.231 1.786 1.247 1.438 1.014 1.433 1.550 1.520
2441.269 1.248 1.321 1.251 1.231 1.785 1.246 1.438 1.013 1.432 1.549 1.519
2451.269 1.248 1.321 1.250 1.230 1.784 1.245 1.438 1.012 1.431 1.548 1.519
2461.268 1.249 1.321 1.250 1.230 1.783 1.245 1.438 1.011 1.430 1.548 1.519
2471.268 1.249 1.321 1.250 1.230 1.783 1.244 1.438 1.011 1.429 1.547 1.519
2481.267 1.249 1.321 1.250 1.230 1.782 1.243 1.438 1.010 1.429 1.546 1.519
2491.267 1.250 1.321 1.250 1.230 1.781 1.243 1.438 1.009 1.428 1.546 1.518
2501.267 1.250 1.321 1.250 1.230 1.781 1.243 1.438 1.009 1.428 1.545 1.518
Data for figure immediately follows

Data for Appendix 4 - Long Memory Hypothesis Tests: Equity (United Arab Emirates - Netherlands)

xiUAEAustraliaBelgiumCanadaCzech RepublicDenmarkFranceGermanyHungaryItalyJapanNetherlands
02.239 1.516 2.055 1.118 2.072 2.094 1.562 1.578 1.494 1.888 2.047 1.404
12.164 1.449 1.923 1.047 1.975 2.043 1.543 1.587 1.439 1.742 1.962 1.404
22.155 1.441 1.864 1.027 1.925 2.027 1.536 1.590 1.405 1.716 1.954 1.404
32.155 1.420 1.849 1.016 1.897 2.014 1.550 1.596 1.403 1.696 1.949 1.415
42.131 1.396 1.839 1.009 1.870 1.994 1.552 1.592 1.395 1.672 1.941 1.413
52.079 1.374 1.842 1.004 1.858 1.984 1.560 1.597 1.392 1.655 1.938 1.417
62.022 1.364 1.848 0.999 1.850 1.976 1.569 1.609 1.389 1.645 1.943 1.424
71.976 1.351 1.854 0.994 1.848 1.969 1.582 1.619 1.391 1.638 1.947 1.430
81.935 1.339 1.855 0.990 1.846 1.958 1.588 1.624 1.388 1.633 1.952 1.426
91.906 1.329 1.850 0.988 1.839 1.943 1.589 1.626 1.384 1.626 1.954 1.417
101.884 1.319 1.847 0.985 1.828 1.930 1.594 1.630 1.376 1.617 1.953 1.411
111.859 1.307 1.841 0.983 1.816 1.914 1.594 1.628 1.365 1.607 1.953 1.401
121.837 1.295 1.841 0.980 1.805 1.903 1.594 1.625 1.352 1.599 1.952 1.395
131.816 1.282 1.837 0.977 1.791 1.892 1.590 1.623 1.340 1.591 1.950 1.389
141.799 1.273 1.828 0.974 1.779 1.880 1.583 1.617 1.328 1.580 1.949 1.384
151.786 1.263 1.817 0.970 1.766 1.868 1.574 1.610 1.317 1.569 1.948 1.376
161.773 1.254 1.810 0.967 1.752 1.857 1.564 1.605 1.307 1.558 1.944 1.369
171.761 1.247 1.806 0.964 1.740 1.849 1.557 1.601 1.298 1.550 1.939 1.366
181.751 1.241 1.805 0.961 1.730 1.844 1.553 1.599 1.289 1.543 1.932 1.365
191.745 1.236 1.804 0.958 1.721 1.840 1.551 1.599 1.281 1.537 1.926 1.365
201.743 1.232 1.803 0.956 1.715 1.836 1.548 1.600 1.274 1.530 1.920 1.364
211.742 1.228 1.803 0.953 1.711 1.833 1.546 1.600 1.268 1.524 1.916 1.364
221.741 1.224 1.802 0.951 1.707 1.830 1.544 1.598 1.264 1.519 1.913 1.363
231.740 1.220 1.800 0.948 1.703 1.828 1.542 1.597 1.259 1.513 1.911 1.362
241.740 1.217 1.798 0.946 1.699 1.826 1.539 1.595 1.255 1.508 1.909 1.359
251.743 1.214 1.798 0.943 1.695 1.824 1.535 1.592 1.249 1.504 1.905 1.358
261.747 1.212 1.797 0.941 1.690 1.823 1.533 1.590 1.244 1.500 1.903 1.358
271.750 1.211 1.797 0.939 1.685 1.822 1.531 1.590 1.239 1.497 1.899 1.358
281.751 1.210 1.797 0.938 1.679 1.821 1.530 1.589 1.234 1.494 1.895 1.359
291.750 1.210 1.795 0.937 1.674 1.819 1.527 1.587 1.229 1.492 1.892 1.357
301.749 1.210 1.793 0.935 1.669 1.819 1.524 1.585 1.225 1.489 1.890 1.356
311.748 1.209 1.791 0.934 1.664 1.818 1.521 1.582 1.222 1.488 1.887 1.354
321.747 1.210 1.790 0.933 1.660 1.817 1.518 1.579 1.220 1.487 1.886 1.351
331.746 1.210 1.789 0.932 1.657 1.817 1.516 1.576 1.218 1.486 1.886 1.349
341.744 1.210 1.787 0.931 1.655 1.817 1.515 1.574 1.218 1.486 1.884 1.347
351.741 1.210 1.784 0.930 1.653 1.818 1.514 1.571 1.217 1.487 1.881 1.345
361.737 1.211 1.781 0.930 1.651 1.819 1.514 1.568 1.216 1.489 1.878 1.344
371.732 1.211 1.778 0.929 1.649 1.821 1.513 1.567 1.215 1.491 1.876 1.342
381.728 1.212 1.777 0.928 1.648 1.822 1.512 1.565 1.215 1.492 1.873 1.341
391.724 1.213 1.775 0.928 1.647 1.823 1.511 1.563 1.215 1.494 1.871 1.339
401.716 1.213 1.774 0.927 1.645 1.822 1.510 1.562 1.215 1.496 1.868 1.338
411.708 1.214 1.772 0.926 1.643 1.820 1.510 1.560 1.214 1.498 1.865 1.337
421.699 1.216 1.770 0.926 1.642 1.818 1.509 1.559 1.214 1.499 1.862 1.335
431.691 1.217 1.768 0.926 1.641 1.816 1.509 1.557 1.213 1.499 1.859 1.334
441.682 1.218 1.765 0.926 1.639 1.813 1.508 1.556 1.213 1.498 1.854 1.332
451.673 1.220 1.762 0.925 1.637 1.811 1.507 1.554 1.213 1.498 1.850 1.331
461.664 1.221 1.760 0.925 1.636 1.808 1.507 1.553 1.213 1.498 1.846 1.329
471.655 1.222 1.757 0.924 1.634 1.806 1.506 1.551 1.213 1.498 1.841 1.328
481.647 1.224 1.755 0.924 1.634 1.804 1.506 1.550 1.214 1.498 1.838 1.327
491.639 1.225 1.753 0.924 1.633 1.803 1.506 1.549 1.215 1.499 1.834 1.327
501.630 1.227 1.751 0.924 1.633 1.801 1.505 1.548 1.215 1.499 1.831 1.327
511.621 1.228 1.750 0.924 1.633 1.798 1.503 1.545 1.216 1.499 1.827 1.327
521.612 1.230 1.749 0.925 1.633 1.796 1.501 1.544 1.216 1.499 1.824 1.326
531.603 1.232 1.748 0.925 1.633 1.794 1.499 1.541 1.216 1.500 1.821 1.326
541.595 1.233 1.746 0.925 1.634 1.792 1.496 1.539 1.215 1.500 1.818 1.325
551.587 1.234 1.745 0.925 1.634 1.789 1.493 1.536 1.215 1.500 1.815 1.325
561.580 1.236 1.743 0.925 1.633 1.788 1.490 1.533 1.214 1.501 1.813 1.324
571.572 1.237 1.742 0.925 1.633 1.786 1.488 1.531 1.214 1.502 1.811 1.324
581.565 1.239 1.741 0.925 1.633 1.784 1.486 1.530 1.214 1.502 1.809 1.323
591.559 1.240 1.741 0.926 1.633 1.783 1.484 1.528 1.214 1.503 1.806 1.323
601.552 1.242 1.741 0.926 1.633 1.782 1.483 1.527 1.214 1.503 1.804 1.323
611.547 1.243 1.741 0.926 1.634 1.782 1.482 1.526 1.214 1.503 1.803 1.323
621.542 1.244 1.741 0.927 1.635 1.781 1.482 1.526 1.215 1.504 1.801 1.324
631.536 1.245 1.740 0.926 1.636 1.780 1.481 1.525 1.216 1.504 1.798 1.324
641.531 1.246 1.740 0.926 1.638 1.779 1.480 1.524 1.217 1.504 1.796 1.324
651.526 1.247 1.739 0.926 1.640 1.777 1.478 1.523 1.217 1.503 1.794 1.324
661.521 1.248 1.739 0.925 1.642 1.775 1.476 1.522 1.217 1.502 1.791 1.324
671.517 1.249 1.739 0.925 1.643 1.773 1.475 1.521 1.218 1.500 1.789 1.324
681.513 1.250 1.739 0.925 1.645 1.771 1.473 1.520 1.218 1.499 1.787 1.324
691.508 1.251 1.738 0.925 1.646 1.768 1.472 1.519 1.218 1.497 1.785 1.324
701.503 1.252 1.738 0.924 1.647 1.766 1.470 1.518 1.218 1.496 1.782 1.323
711.499 1.252 1.738 0.924 1.648 1.763 1.469 1.517 1.218 1.494 1.780 1.323
721.494 1.253 1.738 0.924 1.649 1.761 1.468 1.516 1.218 1.491 1.778 1.323
731.490 1.254 1.739 0.924 1.650 1.758 1.467 1.515 1.218 1.489 1.776 1.324
741.485 1.254 1.739 0.925 1.651 1.755 1.466 1.515 1.218 1.487 1.773 1.324
751.481 1.255 1.739 0.925 1.651 1.753 1.466 1.515 1.218 1.486 1.771 1.324
761.477 1.255 1.739 0.924 1.652 1.750 1.466 1.514 1.218 1.484 1.768 1.324
771.472 1.256 1.739 0.924 1.653 1.747 1.465 1.514 1.219 1.482 1.766 1.324
781.468 1.256 1.738 0.924 1.653 1.744 1.465 1.513 1.219 1.481 1.763 1.324
791.464 1.257 1.738 0.923 1.655 1.741 1.464 1.513 1.219 1.479 1.761 1.324
801.460 1.257 1.736 0.923 1.656 1.738 1.464 1.512 1.219 1.478 1.759 1.324
811.455 1.258 1.736 0.923 1.658 1.736 1.463 1.511 1.219 1.476 1.756 1.325
821.451 1.258 1.735 0.922 1.659 1.734 1.463 1.511 1.219 1.475 1.753 1.325
831.446 1.259 1.734 0.922 1.660 1.731 1.463 1.510 1.219 1.474 1.751 1.325
841.442 1.260 1.733 0.921 1.661 1.729 1.463 1.510 1.219 1.473 1.748 1.326
851.437 1.260 1.732 0.921 1.663 1.727 1.463 1.509 1.219 1.471 1.746 1.326
861.433 1.261 1.731 0.920 1.664 1.725 1.463 1.508 1.220 1.470 1.743 1.326
871.428 1.261 1.729 0.920 1.664 1.722 1.462 1.507 1.220 1.468 1.740 1.326
881.424 1.262 1.728 0.919 1.665 1.720 1.462 1.506 1.220 1.466 1.737 1.326
891.419 1.262 1.727 0.918 1.665 1.717 1.462 1.505 1.219 1.464 1.735 1.326
901.415 1.262 1.725 0.918 1.666 1.714 1.461 1.504 1.219 1.463 1.732 1.326
911.411 1.263 1.724 0.917 1.666 1.711 1.460 1.503 1.219 1.461 1.729 1.326
921.407 1.263 1.722 0.917 1.667 1.708 1.460 1.502 1.219 1.459 1.727 1.327
931.403 1.263 1.721 0.917 1.667 1.706 1.461 1.501 1.219 1.458 1.724 1.328
941.399 1.264 1.720 0.916 1.668 1.703 1.461 1.500 1.219 1.456 1.722 1.328
951.396 1.264 1.719 0.916 1.668 1.701 1.461 1.500 1.219 1.455 1.720 1.329
961.392 1.265 1.718 0.916 1.669 1.698 1.462 1.500 1.219 1.455 1.718 1.330
971.388 1.266 1.717 0.915 1.669 1.696 1.463 1.499 1.219 1.454 1.716 1.331
981.385 1.266 1.716 0.915 1.670 1.693 1.463 1.499 1.219 1.453 1.714 1.332
991.381 1.267 1.715 0.915 1.670 1.691 1.463 1.498 1.219 1.453 1.712 1.333
1001.377 1.267 1.713 0.915 1.670 1.689 1.464 1.498 1.219 1.452 1.710 1.334
1011.373 1.268 1.712 0.915 1.671 1.687 1.464 1.497 1.218 1.451 1.708 1.335
1021.370 1.269 1.711 0.914 1.670 1.685 1.465 1.497 1.218 1.451 1.707 1.336
1031.366 1.269 1.710 0.914 1.670 1.683 1.466 1.497 1.218 1.450 1.705 1.337
1041.362 1.269 1.709 0.914 1.670 1.681 1.466 1.497 1.218 1.450 1.703 1.338
1051.359 1.270 1.709 0.913 1.669 1.679 1.466 1.497 1.218 1.450 1.702 1.339
1061.355 1.270 1.708 0.913 1.668 1.677 1.467 1.496 1.218 1.450 1.700 1.340
1071.352 1.271 1.707 0.913 1.667 1.675 1.468 1.496 1.218 1.449 1.699 1.341
1081.348 1.272 1.706 0.912 1.666 1.673 1.468 1.496 1.218 1.449 1.697 1.342
1091.345 1.272 1.705 0.912 1.665 1.670 1.468 1.495 1.218 1.449 1.696 1.342
1101.341 1.273 1.703 0.911 1.665 1.667 1.468 1.494 1.218 1.448 1.694 1.343
1111.337 1.273 1.701 0.911 1.664 1.664 1.467 1.493 1.217 1.448 1.692 1.343
1121.334 1.274 1.700 0.910 1.662 1.661 1.467 1.492 1.217 1.447 1.690 1.343
1131.330 1.274 1.698 0.910 1.661 1.657 1.466 1.491 1.217 1.447 1.688 1.343
1141.327 1.274 1.696 0.910 1.660 1.654 1.466 1.490 1.217 1.446 1.686 1.344
1151.323 1.275 1.695 0.909 1.659 1.651 1.466 1.489 1.217 1.445 1.684 1.344
1161.319 1.275 1.694 0.909 1.657 1.648 1.466 1.488 1.217 1.445 1.682 1.345
1171.315 1.276 1.692 0.908 1.656 1.645 1.465 1.487 1.217 1.444 1.680 1.345
1181.311 1.276 1.691 0.908 1.655 1.642 1.465 1.487 1.216 1.443 1.678 1.346
1191.307 1.277 1.690 0.907 1.654 1.638 1.464 1.486 1.216 1.443 1.676 1.346
1201.303 1.277 1.689 0.907 1.652 1.635 1.464 1.485 1.215 1.442 1.675 1.346
1211.299 1.277 1.688 0.906 1.650 1.632 1.464 1.485 1.215 1.441 1.673 1.346
1221.296 1.278 1.687 0.906 1.649 1.628 1.463 1.484 1.214 1.440 1.672 1.346
1231.292 1.278 1.686 0.905 1.647 1.625 1.463 1.483 1.213 1.439 1.671 1.346
1241.288 1.279 1.685 0.905 1.645 1.621 1.462 1.482 1.212 1.438 1.670 1.346
1251.285 1.279 1.683 0.904 1.643 1.618 1.461 1.481 1.212 1.437 1.669 1.346
1261.281 1.280 1.682 0.904 1.641 1.614 1.460 1.480 1.211 1.437 1.668 1.345
1271.277 1.281 1.681 0.903 1.639 1.611 1.459 1.479 1.211 1.436 1.667 1.345
1281.274 1.282 1.679 0.903 1.637 1.608 1.459 1.478 1.210 1.435 1.666 1.345
1291.271 1.282 1.678 0.902 1.636 1.604 1.458 1.477 1.209 1.435 1.665 1.345
1301.267 1.283 1.677 0.902 1.634 1.601 1.457 1.476 1.209 1.434 1.663 1.345
1311.264 1.284 1.676 0.901 1.632 1.598 1.457 1.475 1.208 1.432 1.662 1.345
1321.260 1.284 1.675 0.900 1.631 1.595 1.456 1.474 1.207 1.431 1.661 1.345
1331.257 1.285 1.674 0.900 1.629 1.593 1.455 1.473 1.207 1.430 1.660 1.345
1341.254 1.285 1.673 0.899 1.627 1.590 1.453 1.472 1.206 1.429 1.659 1.344
1351.251 1.286 1.671 0.898 1.625 1.587 1.452 1.471 1.205 1.427 1.658 1.344
1361.248 1.286 1.670 0.898 1.623 1.585 1.451 1.470 1.204 1.426 1.657 1.344
1371.244 1.287 1.669 0.897 1.622 1.582 1.450 1.469 1.203 1.425 1.656 1.344
1381.241 1.287 1.668 0.897 1.620 1.580 1.449 1.468 1.202 1.424 1.655 1.343
1391.238 1.288 1.667 0.897 1.618 1.577 1.449 1.467 1.201 1.423 1.654 1.343
1401.235 1.288 1.666 0.896 1.617 1.575 1.448 1.466 1.200 1.422 1.654 1.343
1411.232 1.288 1.665 0.896 1.615 1.573 1.447 1.465 1.199 1.421 1.653 1.343
1421.229 1.289 1.665 0.895 1.614 1.571 1.446 1.464 1.198 1.420 1.652 1.343
1431.226 1.289 1.665 0.895 1.612 1.568 1.446 1.464 1.197 1.419 1.651 1.344
1441.223 1.290 1.664 0.895 1.611 1.566 1.445 1.463 1.196 1.418 1.650 1.344
1451.221 1.290 1.664 0.894 1.609 1.565 1.445 1.463 1.195 1.417 1.650 1.344
1461.218 1.291 1.664 0.894 1.608 1.563 1.444 1.463 1.194 1.417 1.649 1.344
1471.215 1.291 1.663 0.894 1.607 1.561 1.444 1.463 1.193 1.416 1.648 1.345
1481.213 1.292 1.663 0.893 1.605 1.559 1.444 1.463 1.192 1.415 1.647 1.345
1491.210 1.293 1.662 0.893 1.603 1.558 1.443 1.462 1.191 1.414 1.647 1.346
1501.207 1.293 1.662 0.892 1.602 1.556 1.442 1.462 1.190 1.413 1.646 1.346
1511.205 1.294 1.661 0.892 1.600 1.555 1.442 1.462 1.189 1.413 1.645 1.346
1521.203 1.294 1.660 0.891 1.598 1.553 1.441 1.461 1.187 1.412 1.644 1.346
1531.200 1.295 1.660 0.891 1.597 1.552 1.440 1.461 1.186 1.411 1.643 1.347
1541.198 1.296 1.659 0.891 1.595 1.550 1.439 1.460 1.185 1.410 1.642 1.347
1551.196 1.296 1.658 0.890 1.593 1.548 1.439 1.460 1.183 1.409 1.641 1.347
1561.194 1.297 1.658 0.890 1.592 1.547 1.438 1.459 1.182 1.407 1.640 1.347
1571.192 1.298 1.657 0.889 1.590 1.545 1.437 1.459 1.181 1.406 1.639 1.347
1581.190 1.298 1.656 0.889 1.589 1.544 1.437 1.458 1.179 1.405 1.639 1.348
1591.188 1.299 1.655 0.889 1.588 1.542 1.436 1.458 1.178 1.404 1.638 1.348
1601.186 1.299 1.655 0.889 1.586 1.541 1.436 1.458 1.177 1.403 1.637 1.349
1611.184 1.300 1.654 0.888 1.585 1.539 1.436 1.457 1.176 1.402 1.636 1.349
1621.183 1.300 1.654 0.888 1.584 1.538 1.435 1.457 1.175 1.401 1.635 1.349
1631.181 1.301 1.653 0.888 1.583 1.536 1.434 1.456 1.174 1.400 1.634 1.350
1641.179 1.301 1.653 0.887 1.581 1.534 1.433 1.456 1.172 1.400 1.633 1.350
1651.178 1.302 1.651 0.887 1.580 1.533 1.432 1.455 1.171 1.399 1.632 1.350
1661.176 1.302 1.650 0.887 1.579 1.531 1.431 1.454 1.170 1.398 1.631 1.349
1671.174 1.302 1.649 0.886 1.577 1.529 1.430 1.453 1.169 1.397 1.630 1.349
1681.173 1.303 1.648 0.886 1.576 1.528 1.429 1.452 1.167 1.396 1.629 1.349
1691.171 1.303 1.647 0.885 1.575 1.526 1.428 1.451 1.166 1.395 1.628 1.349
1701.170 1.303 1.646 0.885 1.574 1.525 1.427 1.451 1.165 1.394 1.628 1.349
1711.168 1.303 1.645 0.885 1.573 1.523 1.426 1.450 1.164 1.394 1.627 1.349
1721.167 1.304 1.643 0.885 1.573 1.522 1.425 1.449 1.162 1.393 1.627 1.349
1731.165 1.304 1.642 0.884 1.572 1.521 1.424 1.448 1.161 1.392 1.626 1.349
1741.164 1.305 1.641 0.884 1.571 1.520 1.423 1.447 1.160 1.391 1.626 1.349
1751.162 1.305 1.640 0.884 1.571 1.519 1.422 1.446 1.159 1.391 1.625 1.349
1761.161 1.306 1.639 0.884 1.570 1.518 1.421 1.446 1.158 1.390 1.624 1.350
1771.159 1.306 1.639 0.883 1.570 1.517 1.421 1.445 1.157 1.389 1.623 1.350
1781.158 1.307 1.638 0.883 1.569 1.516 1.420 1.445 1.156 1.389 1.622 1.350
1791.157 1.307 1.637 0.883 1.568 1.515 1.419 1.444 1.155 1.388 1.621 1.351
1801.155 1.307 1.636 0.883 1.568 1.514 1.418 1.444 1.154 1.388 1.621 1.351
1811.154 1.308 1.635 0.883 1.567 1.513 1.418 1.443 1.153 1.387 1.620 1.351
1821.153 1.308 1.634 0.882 1.566 1.512 1.417 1.443 1.153 1.386 1.619 1.351
1831.152 1.308 1.634 0.882 1.566 1.511 1.417 1.443 1.152 1.386 1.618 1.352
1841.150 1.309 1.633 0.882 1.565 1.510 1.416 1.443 1.151 1.385 1.618 1.352
1851.149 1.309 1.632 0.882 1.565 1.509 1.416 1.442 1.150 1.385 1.617 1.352
1861.148 1.309 1.632 0.882 1.564 1.508 1.415 1.442 1.150 1.384 1.616 1.352
1871.147 1.310 1.631 0.881 1.564 1.507 1.415 1.442 1.149 1.384 1.615 1.353
1881.146 1.310 1.630 0.881 1.564 1.506 1.414 1.441 1.148 1.383 1.615 1.353
1891.145 1.311 1.629 0.881 1.563 1.505 1.413 1.441 1.148 1.383 1.614 1.353
1901.144 1.311 1.628 0.881 1.563 1.504 1.413 1.440 1.147 1.382 1.613 1.352
1911.143 1.311 1.627 0.881 1.562 1.503 1.412 1.440 1.146 1.382 1.612 1.352
1921.142 1.311 1.626 0.881 1.562 1.502 1.411 1.439 1.146 1.382 1.611 1.352
1931.141 1.312 1.625 0.881 1.561 1.501 1.410 1.439 1.146 1.381 1.610 1.352
1941.141 1.312 1.624 0.881 1.561 1.500 1.410 1.439 1.145 1.381 1.609 1.352
1951.140 1.312 1.623 0.880 1.560 1.499 1.409 1.439 1.144 1.380 1.608 1.352
1961.139 1.312 1.622 0.880 1.560 1.497 1.409 1.438 1.144 1.379 1.607 1.352
1971.138 1.312 1.621 0.880 1.559 1.496 1.408 1.438 1.143 1.378 1.606 1.351
1981.137 1.313 1.620 0.879 1.558 1.495 1.408 1.438 1.142 1.377 1.606 1.351
1991.136 1.313 1.619 0.879 1.558 1.493 1.407 1.437 1.142 1.377 1.605 1.351
2001.136 1.313 1.618 0.879 1.557 1.492 1.406 1.437 1.142 1.376 1.604 1.350
2011.135 1.313 1.617 0.878 1.556 1.491 1.405 1.436 1.141 1.375 1.603 1.350
2021.134 1.313 1.615 0.878 1.556 1.489 1.405 1.436 1.141 1.374 1.602 1.350
2031.133 1.313 1.614 0.878 1.555 1.488 1.404 1.436 1.140 1.373 1.601 1.349
2041.132 1.313 1.613 0.878 1.555 1.487 1.404 1.436 1.140 1.373 1.600 1.349
2051.132 1.313 1.612 0.878 1.554 1.486 1.403 1.435 1.140 1.372 1.599 1.349
2061.131 1.313 1.611 0.878 1.554 1.485 1.402 1.435 1.139 1.371 1.598 1.348
2071.130 1.313 1.609 0.877 1.553 1.484 1.402 1.435 1.138 1.370 1.597 1.348
2081.129 1.313 1.608 0.877 1.553 1.483 1.401 1.434 1.138 1.369 1.596 1.347
2091.128 1.313 1.607 0.877 1.552 1.481 1.401 1.434 1.137 1.369 1.596 1.347
2101.128 1.313 1.606 0.877 1.551 1.480 1.400 1.434 1.137 1.368 1.595 1.346
2111.127 1.314 1.605 0.877 1.550 1.479 1.400 1.434 1.137 1.367 1.594 1.345
2121.126 1.314 1.604 0.877 1.550 1.478 1.399 1.433 1.136 1.366 1.593 1.345
2131.125 1.314 1.603 0.876 1.549 1.477 1.399 1.433 1.136 1.365 1.592 1.344
2141.124 1.314 1.602 0.876 1.548 1.476 1.399 1.433 1.136 1.365 1.591 1.343
2151.124 1.314 1.602 0.876 1.547 1.475 1.398 1.433 1.136 1.364 1.590 1.343
2161.123 1.314 1.600 0.876 1.547 1.474 1.398 1.433 1.136 1.363 1.589 1.342
2171.122 1.315 1.599 0.876 1.546 1.473 1.397 1.432 1.135 1.362 1.588 1.341
2181.121 1.315 1.598 0.876 1.545 1.471 1.396 1.432 1.135 1.361 1.588 1.341
2191.120 1.315 1.597 0.876 1.544 1.470 1.395 1.432 1.135 1.360 1.587 1.340
2201.119 1.315 1.596 0.876 1.543 1.469 1.394 1.431 1.135 1.359 1.585 1.339
2211.119 1.316 1.595 0.876 1.542 1.467 1.394 1.431 1.134 1.358 1.584 1.338
2221.118 1.316 1.593 0.875 1.541 1.466 1.393 1.430 1.134 1.357 1.584 1.337
2231.117 1.316 1.592 0.875 1.540 1.465 1.392 1.430 1.134 1.357 1.583 1.336
2241.116 1.317 1.591 0.875 1.539 1.464 1.391 1.429 1.134 1.356 1.582 1.335
2251.116 1.317 1.590 0.875 1.537 1.463 1.390 1.429 1.133 1.355 1.581 1.334
2261.115 1.317 1.589 0.875 1.536 1.462 1.389 1.428 1.133 1.354 1.580 1.333
2271.115 1.317 1.588 0.874 1.534 1.460 1.389 1.428 1.133 1.353 1.579 1.332
2281.114 1.318 1.587 0.874 1.533 1.459 1.388 1.428 1.133 1.353 1.578 1.332
2291.113 1.318 1.586 0.874 1.532 1.457 1.387 1.428 1.132 1.352 1.577 1.331
2301.113 1.318 1.585 0.874 1.531 1.456 1.386 1.427 1.132 1.352 1.576 1.330
2311.112 1.318 1.584 0.874 1.529 1.454 1.385 1.427 1.132 1.351 1.575 1.329
2321.111 1.319 1.583 0.874 1.528 1.453 1.385 1.427 1.132 1.351 1.574 1.328
2331.111 1.319 1.582 0.873 1.527 1.451 1.384 1.427 1.131 1.350 1.573 1.327
2341.110 1.319 1.581 0.873 1.525 1.450 1.384 1.427 1.131 1.350 1.572 1.327
2351.110 1.320 1.580 0.873 1.524 1.448 1.383 1.426 1.131 1.349 1.571 1.326
2361.109 1.320 1.579 0.873 1.523 1.447 1.382 1.426 1.131 1.349 1.570 1.325
2371.109 1.320 1.578 0.873 1.521 1.446 1.382 1.426 1.130 1.348 1.569 1.324
2381.108 1.321 1.576 0.873 1.520 1.444 1.381 1.425 1.130 1.348 1.568 1.324
2391.108 1.321 1.575 0.873 1.519 1.443 1.380 1.425 1.130 1.347 1.567 1.323
2401.107 1.321 1.574 0.873 1.518 1.442 1.380 1.425 1.130 1.346 1.566 1.322
2411.107 1.321 1.573 0.872 1.517 1.441 1.379 1.424 1.130 1.345 1.565 1.321
2421.107 1.321 1.571 0.872 1.516 1.440 1.378 1.424 1.130 1.345 1.564 1.321
2431.106 1.322 1.570 0.872 1.515 1.439 1.377 1.424 1.130 1.344 1.564 1.320
2441.106 1.322 1.569 0.872 1.515 1.438 1.377 1.423 1.130 1.343 1.563 1.319
2451.105 1.322 1.568 0.872 1.514 1.437 1.376 1.423 1.130 1.342 1.562 1.319
2461.105 1.322 1.567 0.872 1.513 1.436 1.376 1.423 1.130 1.342 1.561 1.318
2471.104 1.322 1.566 0.872 1.512 1.435 1.375 1.423 1.130 1.341 1.560 1.318
2481.104 1.322 1.565 0.872 1.512 1.434 1.374 1.423 1.130 1.340 1.559 1.317
2491.103 1.322 1.564 0.872 1.511 1.434 1.374 1.423 1.129 1.339 1.558 1.317
2501.103 1.322 1.563 0.871 1.511 1.433 1.373 1.422 1.129 1.339 1.557 1.316
Data for figure immediately follows

Data for Appendix 4 - Long Memory Hypothesis Tests: Equity (Norway - United States)

xiNorwayNew ZealandPolandSwedenSpainSwitzerlandUnited KingomUnited States
02.135 1.070 1.453 1.929 1.652 1.509 1.194 1.594
12.114 1.031 1.370 1.940 1.630 1.489 1.182 1.551
22.106 1.014 1.347 1.933 1.633 1.483 1.177 1.549
32.096 1.006 1.335 1.946 1.648 1.490 1.183 1.555
42.068 0.999 1.326 1.955 1.653 1.488 1.172 1.566
52.056 0.993 1.323 1.971 1.659 1.496 1.169 1.572
62.044 0.989 1.325 1.989 1.666 1.505 1.169 1.581
72.033 0.988 1.326 1.996 1.670 1.517 1.169 1.592
82.019 0.988 1.325 1.994 1.668 1.524 1.164 1.601
92.004 0.987 1.319 1.986 1.665 1.527 1.156 1.609
101.990 0.984 1.309 1.986 1.661 1.529 1.150 1.615
111.974 0.981 1.300 1.985 1.654 1.525 1.142 1.620
121.963 0.980 1.292 1.985 1.650 1.523 1.136 1.623
131.950 0.977 1.283 1.984 1.643 1.517 1.131 1.624
141.938 0.974 1.273 1.983 1.635 1.511 1.127 1.624
151.927 0.972 1.265 1.981 1.625 1.504 1.121 1.622
161.918 0.970 1.258 1.975 1.614 1.500 1.117 1.620
171.910 0.969 1.253 1.972 1.606 1.498 1.114 1.618
181.902 0.968 1.249 1.970 1.602 1.499 1.113 1.618
191.894 0.968 1.246 1.973 1.598 1.500 1.113 1.617
201.884 0.967 1.245 1.978 1.593 1.499 1.114 1.618
211.876 0.966 1.244 1.984 1.589 1.496 1.114 1.619
221.867 0.964 1.243 1.984 1.585 1.494 1.114 1.621
231.860 0.963 1.241 1.985 1.581 1.492 1.113 1.622
241.854 0.962 1.239 1.981 1.578 1.489 1.113 1.624
251.846 0.961 1.236 1.977 1.574 1.487 1.113 1.625
261.839 0.960 1.233 1.975 1.572 1.485 1.113 1.628
271.832 0.960 1.230 1.974 1.571 1.484 1.113 1.631
281.826 0.960 1.229 1.973 1.570 1.483 1.114 1.632
291.821 0.962 1.228 1.970 1.567 1.483 1.114 1.632
301.816 0.963 1.228 1.965 1.565 1.481 1.113 1.632
311.812 0.964 1.228 1.962 1.564 1.478 1.114 1.631
321.807 0.965 1.228 1.960 1.561 1.476 1.114 1.630
331.804 0.966 1.228 1.958 1.560 1.473 1.115 1.628
341.801 0.966 1.227 1.958 1.559 1.471 1.117 1.626
351.799 0.967 1.227 1.960 1.559 1.469 1.119 1.626
361.795 0.969 1.226 1.960 1.560 1.466 1.121 1.625
371.793 0.971 1.225 1.962 1.561 1.465 1.123 1.625
381.791 0.973 1.224 1.963 1.561 1.465 1.125 1.624
391.788 0.976 1.222 1.963 1.562 1.465 1.127 1.625
401.785 0.978 1.219 1.963 1.562 1.465 1.128 1.625
411.782 0.980 1.217 1.962 1.563 1.465 1.130 1.627
421.778 0.982 1.215 1.961 1.564 1.465 1.132 1.628
431.775 0.985 1.213 1.960 1.564 1.464 1.134 1.629
441.772 0.986 1.212 1.959 1.563 1.464 1.136 1.630
451.769 0.988 1.211 1.957 1.563 1.463 1.138 1.631
461.766 0.989 1.210 1.955 1.563 1.463 1.141 1.631
471.763 0.990 1.210 1.954 1.563 1.462 1.142 1.632
481.759 0.992 1.210 1.956 1.564 1.462 1.145 1.632
491.755 0.993 1.210 1.959 1.565 1.462 1.147 1.633
501.752 0.995 1.209 1.962 1.566 1.461 1.149 1.634
511.748 0.997 1.208 1.964 1.567 1.461 1.151 1.636
521.745 0.998 1.207 1.966 1.567 1.460 1.153 1.637
531.742 0.999 1.205 1.966 1.567 1.459 1.154 1.639
541.739 1.000 1.203 1.966 1.567 1.459 1.155 1.639
551.736 1.000 1.202 1.966 1.567 1.458 1.156 1.640
561.732 1.000 1.202 1.964 1.567 1.457 1.157 1.641
571.729 1.001 1.202 1.963 1.567 1.457 1.158 1.642
581.726 1.002 1.202 1.961 1.567 1.457 1.159 1.644
591.723 1.004 1.202 1.959 1.567 1.456 1.160 1.645
601.720 1.005 1.203 1.957 1.568 1.457 1.161 1.646
611.718 1.007 1.203 1.955 1.569 1.458 1.162 1.647
621.716 1.008 1.204 1.953 1.570 1.459 1.164 1.648
631.715 1.010 1.204 1.951 1.571 1.460 1.165 1.648
641.713 1.012 1.205 1.949 1.572 1.461 1.166 1.648
651.710 1.013 1.205 1.946 1.572 1.460 1.167 1.648
661.707 1.014 1.206 1.944 1.572 1.460 1.168 1.648
671.704 1.015 1.206 1.941 1.572 1.461 1.169 1.648
681.701 1.016 1.206 1.937 1.572 1.461 1.169 1.649
691.698 1.016 1.206 1.935 1.572 1.461 1.170 1.649
701.695 1.017 1.207 1.932 1.571 1.461 1.171 1.649
711.692 1.017 1.207 1.929 1.572 1.461 1.172 1.650
721.689 1.017 1.208 1.925 1.571 1.461 1.173 1.650
731.685 1.017 1.208 1.923 1.571 1.461 1.174 1.651
741.682 1.017 1.209 1.920 1.571 1.461 1.175 1.652
751.679 1.016 1.209 1.918 1.572 1.461 1.176 1.652
761.676 1.016 1.210 1.917 1.572 1.462 1.177 1.653
771.673 1.015 1.211 1.916 1.572 1.462 1.178 1.652
781.670 1.014 1.211 1.914 1.573 1.462 1.179 1.653
791.667 1.013 1.212 1.912 1.573 1.462 1.180 1.653
801.664 1.012 1.214 1.910 1.572 1.461 1.181 1.653
811.662 1.012 1.215 1.908 1.571 1.460 1.182 1.653
821.659 1.012 1.217 1.906 1.571 1.460 1.182 1.654
831.656 1.012 1.220 1.905 1.571 1.459 1.183 1.654
841.653 1.012 1.222 1.903 1.571 1.459 1.184 1.655
851.651 1.012 1.224 1.902 1.571 1.459 1.185 1.655
861.648 1.012 1.226 1.900 1.570 1.458 1.186 1.656
871.645 1.012 1.227 1.897 1.570 1.458 1.186 1.656
881.642 1.013 1.229 1.895 1.569 1.458 1.187 1.656
891.639 1.013 1.230 1.893 1.568 1.458 1.187 1.656
901.636 1.013 1.232 1.891 1.567 1.457 1.188 1.656
911.634 1.013 1.234 1.889 1.565 1.457 1.188 1.656
921.631 1.013 1.235 1.887 1.564 1.457 1.189 1.657
931.630 1.013 1.237 1.885 1.563 1.457 1.189 1.657
941.628 1.014 1.238 1.883 1.562 1.457 1.189 1.658
951.626 1.015 1.240 1.881 1.562 1.458 1.190 1.659
961.624 1.015 1.241 1.880 1.562 1.458 1.191 1.660
971.623 1.016 1.242 1.878 1.561 1.459 1.192 1.661
981.621 1.017 1.243 1.876 1.561 1.459 1.193 1.662
991.620 1.018 1.245 1.875 1.560 1.459 1.194 1.662
1001.619 1.019 1.246 1.874 1.560 1.458 1.195 1.663
1011.618 1.020 1.246 1.872 1.560 1.458 1.196 1.663
1021.617 1.021 1.247 1.871 1.560 1.458 1.197 1.664
1031.616 1.022 1.246 1.869 1.559 1.457 1.199 1.664
1041.615 1.024 1.246 1.869 1.559 1.457 1.200 1.664
1051.614 1.026 1.246 1.867 1.559 1.457 1.201 1.664
1061.613 1.028 1.245 1.866 1.559 1.456 1.202 1.665
1071.612 1.030 1.245 1.865 1.559 1.456 1.203 1.665
1081.611 1.032 1.245 1.863 1.559 1.455 1.204 1.664
1091.610 1.034 1.244 1.861 1.559 1.454 1.205 1.664
1101.609 1.036 1.244 1.858 1.558 1.452 1.206 1.664
1111.608 1.037 1.243 1.856 1.558 1.451 1.206 1.663
1121.607 1.039 1.242 1.853 1.557 1.450 1.207 1.663
1131.606 1.041 1.241 1.850 1.557 1.448 1.207 1.662
1141.605 1.042 1.241 1.848 1.557 1.447 1.208 1.661
1151.604 1.044 1.240 1.846 1.557 1.446 1.208 1.660
1161.603 1.045 1.239 1.844 1.558 1.445 1.209 1.659
1171.602 1.047 1.238 1.843 1.558 1.444 1.209 1.657
1181.601 1.048 1.238 1.840 1.558 1.442 1.209 1.656
1191.600 1.049 1.237 1.839 1.558 1.441 1.210 1.655
1201.599 1.050 1.237 1.837 1.558 1.440 1.210 1.654
1211.598 1.051 1.236 1.836 1.558 1.439 1.211 1.654
1221.597 1.052 1.236 1.834 1.558 1.437 1.211 1.653
1231.596 1.053 1.235 1.832 1.559 1.436 1.212 1.652
1241.595 1.054 1.235 1.830 1.559 1.435 1.213 1.652
1251.594 1.055 1.234 1.827 1.559 1.433 1.213 1.651
1261.593 1.055 1.233 1.825 1.559 1.432 1.214 1.651
1271.591 1.056 1.233 1.823 1.560 1.431 1.215 1.650
1281.590 1.057 1.232 1.821 1.560 1.429 1.215 1.650
1291.589 1.057 1.232 1.818 1.561 1.428 1.216 1.649
1301.588 1.058 1.231 1.815 1.561 1.427 1.216 1.648
1311.586 1.059 1.231 1.813 1.561 1.425 1.217 1.648
1321.585 1.059 1.230 1.811 1.561 1.424 1.217 1.647
1331.583 1.059 1.229 1.808 1.560 1.423 1.218 1.646
1341.582 1.060 1.229 1.805 1.560 1.422 1.219 1.646
1351.580 1.060 1.228 1.802 1.559 1.421 1.219 1.645
1361.579 1.061 1.227 1.799 1.559 1.420 1.220 1.645
1371.578 1.061 1.226 1.796 1.559 1.419 1.220 1.645
1381.576 1.062 1.226 1.793 1.558 1.418 1.221 1.644
1391.575 1.063 1.225 1.790 1.558 1.417 1.222 1.644
1401.574 1.064 1.225 1.787 1.558 1.417 1.222 1.644
1411.573 1.065 1.224 1.785 1.558 1.416 1.223 1.643
1421.572 1.066 1.223 1.782 1.557 1.416 1.223 1.643
1431.571 1.067 1.222 1.780 1.557 1.415 1.224 1.642
1441.570 1.068 1.222 1.778 1.557 1.415 1.224 1.642
1451.569 1.069 1.221 1.776 1.557 1.415 1.225 1.642
1461.568 1.070 1.220 1.774 1.557 1.414 1.225 1.642
1471.567 1.071 1.219 1.772 1.557 1.414 1.226 1.642
1481.567 1.072 1.218 1.771 1.557 1.414 1.226 1.642
1491.566 1.072 1.217 1.769 1.557 1.414 1.227 1.642
1501.565 1.073 1.216 1.768 1.556 1.414 1.227 1.642
1511.564 1.074 1.215 1.766 1.556 1.414 1.228 1.642
1521.563 1.074 1.214 1.765 1.555 1.413 1.228 1.642
1531.563 1.075 1.213 1.763 1.554 1.413 1.228 1.642
1541.562 1.075 1.212 1.761 1.554 1.413 1.229 1.642
1551.561 1.075 1.211 1.760 1.553 1.413 1.229 1.642
1561.559 1.075 1.209 1.759 1.553 1.412 1.229 1.642
1571.558 1.076 1.208 1.758 1.552 1.412 1.230 1.642
1581.557 1.076 1.207 1.757 1.552 1.412 1.230 1.643
1591.556 1.077 1.206 1.755 1.552 1.412 1.231 1.643
1601.555 1.078 1.205 1.754 1.551 1.411 1.231 1.644
1611.553 1.079 1.204 1.753 1.551 1.411 1.232 1.644
1621.552 1.079 1.203 1.751 1.550 1.411 1.232 1.644
1631.551 1.080 1.201 1.749 1.550 1.411 1.233 1.644
1641.550 1.080 1.200 1.747 1.549 1.411 1.234 1.644
1651.549 1.081 1.199 1.745 1.548 1.410 1.234 1.644
1661.547 1.081 1.198 1.743 1.547 1.409 1.234 1.644
1671.546 1.082 1.197 1.741 1.545 1.408 1.235 1.644
1681.545 1.082 1.196 1.738 1.544 1.408 1.235 1.644
1691.543 1.083 1.196 1.736 1.543 1.407 1.235 1.643
1701.542 1.084 1.195 1.734 1.542 1.406 1.236 1.643
1711.540 1.084 1.194 1.732 1.541 1.405 1.236 1.643
1721.539 1.085 1.194 1.731 1.540 1.405 1.237 1.643
1731.538 1.086 1.193 1.730 1.539 1.404 1.237 1.643
1741.537 1.087 1.192 1.728 1.538 1.404 1.238 1.643
1751.535 1.088 1.191 1.726 1.537 1.403 1.238 1.644
1761.534 1.089 1.191 1.725 1.536 1.403 1.239 1.644
1771.533 1.089 1.191 1.724 1.536 1.403 1.240 1.644
1781.531 1.090 1.190 1.722 1.535 1.403 1.241 1.644
1791.530 1.091 1.190 1.721 1.535 1.402 1.242 1.644
1801.529 1.092 1.189 1.720 1.534 1.402 1.242 1.643
1811.527 1.092 1.189 1.720 1.534 1.402 1.243 1.643
1821.526 1.093 1.189 1.718 1.533 1.401 1.244 1.643
1831.525 1.093 1.189 1.718 1.533 1.401 1.245 1.643
1841.524 1.093 1.189 1.717 1.532 1.401 1.246 1.643
1851.522 1.094 1.189 1.716 1.532 1.401 1.247 1.642
1861.521 1.093 1.188 1.715 1.532 1.401 1.249 1.642
1871.520 1.093 1.188 1.714 1.531 1.401 1.250 1.642
1881.518 1.093 1.188 1.713 1.531 1.401 1.251 1.641
1891.517 1.093 1.188 1.711 1.530 1.400 1.253 1.641
1901.516 1.093 1.188 1.710 1.529 1.400 1.254 1.640
1911.515 1.093 1.188 1.708 1.529 1.400 1.255 1.640
1921.513 1.093 1.188 1.707 1.528 1.400 1.256 1.639
1931.512 1.094 1.188 1.705 1.527 1.400 1.258 1.639
1941.511 1.094 1.188 1.704 1.527 1.400 1.259 1.638
1951.509 1.094 1.187 1.702 1.526 1.399 1.260 1.638
1961.507 1.094 1.187 1.701 1.525 1.399 1.261 1.637
1971.506 1.094 1.186 1.699 1.524 1.399 1.262 1.637
1981.504 1.095 1.186 1.698 1.523 1.399 1.263 1.636
1991.503 1.095 1.186 1.697 1.522 1.398 1.264 1.635
2001.501 1.095 1.186 1.695 1.521 1.398 1.265 1.635
2011.500 1.095 1.185 1.694 1.520 1.398 1.266 1.635
2021.498 1.096 1.185 1.692 1.518 1.398 1.267 1.634
2031.497 1.096 1.185 1.691 1.518 1.397 1.268 1.634
2041.496 1.096 1.184 1.690 1.516 1.397 1.269 1.634
2051.494 1.096 1.184 1.688 1.516 1.397 1.270 1.634
2061.493 1.096 1.184 1.687 1.515 1.397 1.271 1.634
2071.492 1.096 1.183 1.686 1.514 1.396 1.272 1.634
2081.490 1.096 1.183 1.685 1.513 1.396 1.274 1.634
2091.489 1.096 1.183 1.683 1.511 1.396 1.275 1.633
2101.488 1.096 1.183 1.682 1.511 1.396 1.276 1.633
2111.486 1.096 1.183 1.681 1.510 1.395 1.277 1.633
2121.485 1.095 1.182 1.680 1.509 1.395 1.278 1.633
2131.484 1.096 1.182 1.679 1.508 1.395 1.279 1.633
2141.482 1.096 1.182 1.679 1.507 1.395 1.280 1.633
2151.481 1.096 1.182 1.678 1.506 1.395 1.281 1.632
2161.480 1.096 1.182 1.677 1.505 1.395 1.282 1.632
2171.478 1.096 1.182 1.676 1.504 1.394 1.283 1.632
2181.477 1.097 1.182 1.675 1.503 1.394 1.283 1.631
2191.476 1.097 1.182 1.674 1.502 1.393 1.284 1.631
2201.474 1.097 1.181 1.673 1.501 1.392 1.285 1.630
2211.473 1.097 1.181 1.671 1.500 1.392 1.285 1.630
2221.472 1.098 1.181 1.670 1.499 1.391 1.286 1.629
2231.470 1.098 1.181 1.669 1.498 1.391 1.286 1.629
2241.469 1.099 1.181 1.668 1.497 1.390 1.286 1.628
2251.468 1.099 1.181 1.666 1.496 1.390 1.287 1.628
2261.467 1.100 1.181 1.665 1.496 1.389 1.287 1.627
2271.466 1.101 1.181 1.664 1.495 1.388 1.287 1.626
2281.464 1.102 1.181 1.662 1.494 1.388 1.288 1.625
2291.463 1.103 1.181 1.661 1.493 1.387 1.288 1.625
2301.462 1.103 1.181 1.660 1.492 1.387 1.288 1.624
2311.461 1.104 1.181 1.659 1.491 1.387 1.289 1.623
2321.460 1.105 1.181 1.657 1.490 1.386 1.289 1.622
2331.459 1.106 1.182 1.656 1.490 1.385 1.289 1.622
2341.458 1.108 1.182 1.655 1.489 1.385 1.289 1.621
2351.457 1.109 1.182 1.654 1.488 1.384 1.289 1.621
2361.456 1.110 1.182 1.653 1.486 1.383 1.289 1.620
2371.455 1.111 1.182 1.652 1.485 1.383 1.289 1.620
2381.454 1.112 1.182 1.651 1.484 1.382 1.289 1.619
2391.453 1.113 1.182 1.650 1.483 1.382 1.290 1.619
2401.452 1.115 1.182 1.650 1.482 1.381 1.290 1.618
2411.452 1.116 1.182 1.649 1.481 1.381 1.290 1.618
2421.451 1.117 1.183 1.648 1.481 1.380 1.290 1.618
2431.450 1.118 1.183 1.648 1.480 1.380 1.290 1.617
2441.449 1.120 1.183 1.647 1.479 1.379 1.290 1.617
2451.448 1.121 1.183 1.646 1.478 1.379 1.290 1.616
2461.447 1.122 1.183 1.645 1.477 1.378 1.290 1.616
2471.447 1.123 1.183 1.645 1.477 1.378 1.291 1.615
2481.446 1.125 1.184 1.644 1.476 1.377 1.291 1.614
2491.445 1.126 1.184 1.643 1.475 1.376 1.291 1.614
2501.445 1.127 1.184 1.643 1.474 1.376 1.292 1.613
Data for figure immediately follows

Data for Appendix 4 - Long Memory Hypothesis Tests: Commodity (Crude Oil - Platnium)

xiCrude OilNatural GasHeating OilGasolineAluminumCopperGoldLeadNickelTinZincPlatinum
00.9481 1.0567 0.9164 0.9639 1.163 1.1766 1.1375 1.2998 1.3357 1.325 0.9784 1.4679
10.9506 1.05 0.9185 1.004 1.2257 1.2152 1.2044 1.3105 1.4214 1.3642 1.0014 1.477
20.9678 1.0405 0.9744 1.0114 1.265 1.2625 1.2375 1.328 1.5003 1.3953 0.9989 1.4939
30.9901 1.0491 0.999 1.0191 1.2789 1.2771 1.2592 1.3308 1.5266 1.4001 0.9967 1.4842
41.0023 1.0594 0.9983 1.0281 1.2945 1.2839 1.2776 1.3338 1.548 1.3955 0.9952 1.4736
51.0151 1.0644 0.9958 1.0377 1.305 1.2963 1.3014 1.3137 1.5665 1.3843 0.9938 1.4758
61.0246 1.0751 1.0015 1.0467 1.3098 1.3178 1.3108 1.2972 1.582 1.3808 0.9964 1.4819
71.0329 1.0869 1.0074 1.0562 1.3193 1.3366 1.3126 1.288 1.5821 1.3738 0.997 1.4855
81.0425 1.1067 1.0138 1.0683 1.3189 1.3438 1.3036 1.2751 1.5754 1.3657 1.0037 1.4805
91.0506 1.1294 1.0186 1.0784 1.3158 1.3462 1.2964 1.2691 1.5642 1.3596 1.0071 1.4799
101.059 1.146 1.0195 1.0938 1.3112 1.3541 1.2934 1.2685 1.5668 1.3529 1.0066 1.4846
111.0632 1.1635 1.02 1.1112 1.3043 1.3623 1.2969 1.2656 1.5801 1.3424 1.0092 1.4907
121.069 1.1703 1.0211 1.1221 1.2928 1.3657 1.2998 1.2639 1.5846 1.3334 1.0104 1.4912
131.0744 1.1774 1.0247 1.1376 1.2838 1.3644 1.3006 1.2594 1.5912 1.3235 1.0147 1.4927
141.0786 1.1782 1.0299 1.1485 1.2763 1.3599 1.2924 1.2549 1.6019 1.3178 1.0155 1.4936
151.0778 1.1763 1.0288 1.1556 1.2724 1.3594 1.2886 1.2528 1.6021 1.3115 1.0162 1.496
161.079 1.174 1.0293 1.1658 1.2648 1.3518 1.2814 1.2528 1.6 1.3022 1.0159 1.4976
171.08 1.1732 1.0327 1.176 1.2593 1.3452 1.2761 1.2512 1.5978 1.2968 1.0137 1.498
181.0794 1.1728 1.0375 1.1825 1.2537 1.344 1.2674 1.2507 1.5969 1.292 1.0114 1.4958
191.0766 1.1682 1.0418 1.1843 1.2461 1.3401 1.2618 1.2495 1.5993 1.2875 1.0082 1.4914
201.0742 1.1639 1.0437 1.1884 1.2403 1.3387 1.2566 1.2508 1.6008 1.2835 1.0056 1.4848
211.0713 1.1622 1.0466 1.1905 1.2337 1.3372 1.2504 1.2525 1.6005 1.2815 1.0013 1.4804
221.0688 1.1626 1.0508 1.194 1.2265 1.3377 1.2436 1.2552 1.6 1.2826 0.9992 1.4746
231.0672 1.1644 1.0562 1.1991 1.2227 1.341 1.2367 1.2585 1.6004 1.2861 0.9988 1.4697
241.0659 1.1662 1.0612 1.2039 1.2175 1.3407 1.23 1.2619 1.5973 1.2889 0.9983 1.4666
251.0643 1.1677 1.0662 1.2079 1.2133 1.3407 1.2266 1.2642 1.5938 1.2915 1 1.4616
261.0621 1.1684 1.0708 1.2086 1.212 1.3433 1.2256 1.2657 1.594 1.2931 1.0024 1.4569
271.0602 1.1711 1.0759 1.2108 1.2102 1.3458 1.2243 1.2668 1.5967 1.2951 1.0051 1.4524
281.0591 1.1744 1.0836 1.2112 1.2076 1.3478 1.2231 1.2681 1.5984 1.296 1.0099 1.4492
291.0587 1.1756 1.0913 1.2115 1.2061 1.3526 1.2225 1.2691 1.6025 1.2979 1.0142 1.4456
301.0576 1.1773 1.0966 1.2139 1.205 1.3565 1.2225 1.2681 1.6037 1.2993 1.0185 1.4421
311.0578 1.1815 1.1019 1.2191 1.2018 1.36 1.2212 1.2672 1.6009 1.2997 1.022 1.4391
321.0577 1.1862 1.1091 1.2257 1.1988 1.3638 1.2209 1.265 1.6013 1.3009 1.0287 1.4359
331.0581 1.1925 1.1163 1.2338 1.1953 1.3664 1.2204 1.2619 1.6003 1.3024 1.0338 1.4345
341.0585 1.1976 1.1212 1.2426 1.1942 1.3694 1.2221 1.2576 1.6015 1.3041 1.0393 1.4347
351.0591 1.2025 1.1257 1.2497 1.1941 1.3714 1.2219 1.2532 1.6047 1.3051 1.0448 1.436
361.0607 1.208 1.1308 1.2588 1.193 1.3716 1.22 1.2484 1.6058 1.306 1.0489 1.4368
371.0618 1.2154 1.1359 1.2687 1.1899 1.3701 1.2193 1.243 1.6057 1.3072 1.0539 1.4368
381.0626 1.2217 1.1405 1.2785 1.1882 1.3683 1.2186 1.2369 1.6063 1.3081 1.0574 1.4369
391.0634 1.2277 1.1445 1.2885 1.1872 1.3676 1.2172 1.2312 1.6032 1.3086 1.0606 1.4361
401.0637 1.2342 1.148 1.2992 1.1845 1.3658 1.217 1.2249 1.5988 1.3089 1.0633 1.435
411.0637 1.2384 1.1511 1.3078 1.1824 1.3642 1.2183 1.2199 1.594 1.3099 1.0671 1.4343
421.0638 1.2431 1.1548 1.3161 1.1812 1.3637 1.2199 1.2137 1.5917 1.3108 1.0699 1.4339
431.0648 1.2468 1.1595 1.3235 1.1809 1.3622 1.2217 1.2081 1.5902 1.3112 1.0715 1.4317
441.0656 1.2524 1.1649 1.3333 1.1809 1.3605 1.2232 1.2025 1.588 1.3124 1.0745 1.4306
451.0655 1.2577 1.1713 1.3394 1.1813 1.3572 1.2242 1.1979 1.5872 1.3136 1.0781 1.4298
461.0651 1.2617 1.1772 1.3436 1.1823 1.3557 1.2257 1.1943 1.5857 1.3153 1.0828 1.429
471.065 1.2666 1.1831 1.3461 1.1834 1.3544 1.2284 1.1915 1.5825 1.317 1.0881 1.4281
481.0646 1.2717 1.1893 1.3496 1.1842 1.3537 1.2316 1.1897 1.5792 1.3169 1.0927 1.4272
491.0642 1.277 1.1959 1.3539 1.1844 1.3523 1.2342 1.1888 1.577 1.3169 1.0977 1.426
501.0644 1.2839 1.2019 1.3588 1.1852 1.353 1.2378 1.189 1.5756 1.3169 1.1038 1.4242
511.0651 1.291 1.207 1.3637 1.1858 1.3545 1.2411 1.1902 1.5743 1.3182 1.1115 1.4223
521.0657 1.2972 1.2126 1.3715 1.1856 1.3558 1.2436 1.191 1.5748 1.3188 1.1199 1.4195
531.0662 1.302 1.2186 1.3789 1.1856 1.3565 1.2471 1.1915 1.5738 1.3199 1.1278 1.418
541.0671 1.3074 1.2239 1.3859 1.1858 1.3572 1.2505 1.1927 1.5703 1.3222 1.1354 1.4163
551.0684 1.3142 1.2289 1.3941 1.1869 1.358 1.2535 1.1936 1.5679 1.3241 1.1429 1.4141
561.07 1.3206 1.2332 1.4016 1.1873 1.359 1.2573 1.195 1.5653 1.3256 1.1503 1.4127
571.0721 1.3273 1.2377 1.4093 1.1878 1.3602 1.2613 1.1961 1.5625 1.3271 1.1576 1.4107
581.0749 1.3338 1.2421 1.417 1.1882 1.3618 1.2645 1.1965 1.5605 1.3278 1.1667 1.4087
591.0771 1.3404 1.2456 1.4258 1.1885 1.3643 1.2672 1.1965 1.5576 1.3285 1.1747 1.4069
601.0793 1.3457 1.2492 1.433 1.1885 1.3665 1.2706 1.1963 1.5559 1.33 1.183 1.4054
611.0816 1.3517 1.2522 1.4407 1.1893 1.3685 1.2743 1.1966 1.5533 1.3311 1.192 1.4034
621.0838 1.3572 1.2551 1.4482 1.1912 1.3705 1.2789 1.1972 1.5511 1.3313 1.2016 1.4019
631.0852 1.3636 1.2583 1.4547 1.1927 1.3737 1.2831 1.1979 1.5484 1.3315 1.2099 1.4007
641.0863 1.3702 1.2619 1.4613 1.1944 1.3767 1.2877 1.1974 1.5476 1.3314 1.2186 1.3992
651.0874 1.3779 1.2641 1.4692 1.1959 1.3787 1.292 1.197 1.5463 1.3309 1.228 1.3966
661.0886 1.3846 1.2663 1.4757 1.1971 1.3798 1.2957 1.1965 1.5452 1.3306 1.2352 1.3952
671.0899 1.3909 1.2684 1.482 1.1986 1.3807 1.2988 1.1958 1.5451 1.3301 1.2424 1.394
681.0911 1.3961 1.2702 1.4877 1.1997 1.3812 1.3023 1.1951 1.5454 1.3289 1.2488 1.3933
691.0913 1.4015 1.2709 1.4943 1.2005 1.3805 1.3064 1.1943 1.5449 1.3273 1.253 1.3915
701.0917 1.4052 1.2708 1.4985 1.2011 1.3797 1.3098 1.1931 1.5434 1.3265 1.2552 1.3902
711.0918 1.4085 1.2703 1.502 1.2019 1.3796 1.3126 1.1921 1.5407 1.3252 1.2572 1.3885
721.0921 1.4102 1.2706 1.501 1.2028 1.3809 1.3155 1.1911 1.5375 1.3237 1.2599 1.3864
731.0927 1.4127 1.2716 1.5022 1.2039 1.382 1.3177 1.1904 1.5355 1.3223 1.2627 1.385
741.0933 1.4145 1.272 1.5027 1.205 1.3828 1.3205 1.1896 1.5337 1.322 1.2659 1.3844
751.0935 1.4144 1.2725 1.5025 1.207 1.3831 1.3231 1.1886 1.5315 1.3213 1.2683 1.3838
761.0944 1.4148 1.2737 1.5018 1.2085 1.3829 1.3271 1.1875 1.5295 1.3203 1.2705 1.3834
771.0953 1.4147 1.2751 1.5006 1.2093 1.3818 1.3305 1.1859 1.5276 1.3197 1.274 1.3824
781.096 1.4167 1.2767 1.5025 1.2105 1.3808 1.3335 1.1845 1.5261 1.3189 1.2771 1.3817
791.0972 1.4201 1.2784 1.5047 1.212 1.3801 1.3363 1.1829 1.5237 1.3182 1.2815 1.3809
801.0986 1.422 1.2801 1.5067 1.2132 1.3794 1.3378 1.1815 1.5221 1.3171 1.2846 1.3797
811.1 1.4248 1.2811 1.5086 1.2144 1.379 1.3402 1.1801 1.5199 1.3163 1.2865 1.3787
821.1012 1.4286 1.2825 1.5126 1.2153 1.3785 1.3412 1.1786 1.5175 1.3159 1.2892 1.3776
831.1025 1.433 1.2846 1.516 1.2172 1.378 1.3417 1.1775 1.5158 1.3151 1.2905 1.3757
841.1038 1.4375 1.2861 1.5179 1.2181 1.3763 1.3422 1.1771 1.5135 1.3136 1.2909 1.3745
851.1053 1.443 1.2872 1.5213 1.2187 1.3745 1.3426 1.1767 1.511 1.312 1.2905 1.3735
861.1067 1.4483 1.288 1.5243 1.2199 1.3728 1.3438 1.1766 1.5089 1.3109 1.2886 1.3724
871.1079 1.4529 1.2886 1.5287 1.2208 1.3706 1.344 1.1764 1.5061 1.3092 1.2869 1.3713
881.1091 1.4566 1.2894 1.5319 1.2218 1.3694 1.3446 1.1764 1.5031 1.3073 1.2851 1.371
891.1101 1.459 1.2894 1.5335 1.2231 1.3678 1.3449 1.1765 1.5003 1.3057 1.2835 1.3706
901.1108 1.4607 1.2895 1.5344 1.2244 1.3658 1.3461 1.1767 1.4986 1.3042 1.2818 1.3709
911.1117 1.4625 1.2896 1.5339 1.2262 1.3645 1.3461 1.1771 1.4973 1.3027 1.2804 1.3709
921.1128 1.4637 1.2896 1.5325 1.2286 1.3645 1.3464 1.1773 1.4961 1.3013 1.2786 1.3708
931.1139 1.4647 1.2897 1.5329 1.2309 1.3652 1.3479 1.1778 1.4955 1.3001 1.2777 1.3714
941.1151 1.4641 1.2905 1.5311 1.2328 1.3656 1.3484 1.1781 1.495 1.2987 1.2761 1.3717
951.1168 1.4644 1.2912 1.5305 1.2354 1.3665 1.3488 1.1785 1.4948 1.297 1.2754 1.3717
961.1188 1.4652 1.2907 1.5312 1.2373 1.3675 1.3491 1.1788 1.4941 1.2955 1.2753 1.3719
971.1207 1.4672 1.2911 1.5347 1.2393 1.3681 1.3496 1.1788 1.4938 1.2942 1.2752 1.3718
981.123 1.4701 1.2916 1.538 1.2415 1.3683 1.3509 1.1791 1.4941 1.2929 1.2766 1.3713
991.125 1.4733 1.2921 1.5418 1.2435 1.369 1.3525 1.179 1.4942 1.2918 1.2774 1.3712
1001.127 1.4768 1.292 1.5452 1.2459 1.3698 1.3543 1.1792 1.4938 1.2906 1.278 1.3709
1011.1288 1.4815 1.2919 1.5494 1.2481 1.3704 1.3561 1.1792 1.4929 1.2892 1.2782 1.3709
1021.1307 1.4854 1.2924 1.5537 1.2504 1.3716 1.3578 1.1791 1.4923 1.288 1.2777 1.3707
1031.1326 1.4906 1.2931 1.5593 1.2531 1.3723 1.3591 1.1793 1.492 1.2869 1.2773 1.3707
1041.1344 1.4954 1.294 1.5642 1.2559 1.3736 1.3616 1.1795 1.4926 1.2863 1.2766 1.3712
1051.1359 1.5006 1.2941 1.5684 1.2591 1.3752 1.3645 1.18 1.4929 1.2857 1.2764 1.3718
1061.1374 1.5051 1.2941 1.5722 1.2624 1.3769 1.3681 1.1805 1.4927 1.2857 1.2759 1.3726
1071.1391 1.5085 1.2945 1.5765 1.2653 1.3791 1.3711 1.1809 1.4927 1.2862 1.2763 1.3729
1081.1402 1.512 1.2956 1.5807 1.2682 1.3822 1.3744 1.1812 1.4926 1.2867 1.2767 1.373
1091.141 1.5134 1.2969 1.5817 1.2707 1.3857 1.3774 1.1818 1.4924 1.287 1.2763 1.3732
1101.1418 1.516 1.2976 1.5831 1.2731 1.3885 1.3803 1.1823 1.4917 1.2876 1.2772 1.3731
1111.1427 1.5187 1.2983 1.5822 1.2754 1.3903 1.3835 1.1827 1.4914 1.2887 1.2785 1.3723
1121.1434 1.5216 1.3 1.5821 1.2775 1.3913 1.3868 1.183 1.4904 1.2893 1.28 1.3715
1131.1446 1.5247 1.3013 1.5817 1.2792 1.3927 1.3884 1.1835 1.4894 1.2898 1.2814 1.3703
1141.1456 1.5282 1.3026 1.5796 1.2809 1.3932 1.3905 1.1842 1.4884 1.2902 1.2828 1.3692
1151.1466 1.532 1.3038 1.5789 1.2827 1.3935 1.393 1.185 1.4876 1.291 1.2849 1.3682
1161.1475 1.5361 1.305 1.5785 1.2845 1.3947 1.396 1.1857 1.4876 1.2921 1.2872 1.3671
1171.1486 1.5415 1.3069 1.5787 1.2865 1.3957 1.3987 1.1865 1.487 1.2929 1.2895 1.3663
1181.1499 1.547 1.3089 1.5791 1.2888 1.3966 1.4018 1.187 1.486 1.2934 1.2916 1.3658
1191.1516 1.5539 1.3104 1.5797 1.2911 1.398 1.405 1.1875 1.4853 1.2938 1.2946 1.3653
1201.1532 1.5612 1.3117 1.5794 1.2934 1.3985 1.4092 1.1882 1.4841 1.2944 1.2993 1.3646
1211.1548 1.5683 1.3133 1.5807 1.295 1.3991 1.4135 1.1883 1.4833 1.2945 1.3042 1.364
1221.1563 1.5755 1.3148 1.5808 1.2964 1.399 1.417 1.1886 1.4824 1.2946 1.3086 1.3631
1231.1577 1.5832 1.3166 1.5803 1.2976 1.3993 1.421 1.1888 1.4817 1.2949 1.3122 1.3624
1241.1594 1.5926 1.3188 1.581 1.2991 1.3994 1.425 1.1889 1.4803 1.295 1.3154 1.3618
1251.161 1.6026 1.3201 1.5832 1.3007 1.3995 1.4288 1.1891 1.4789 1.2952 1.3188 1.3611
1261.1627 1.6113 1.3212 1.5844 1.3025 1.4001 1.4329 1.1895 1.4777 1.295 1.3229 1.3606
1271.1642 1.6203 1.3226 1.5864 1.304 1.4007 1.4365 1.19 1.4763 1.2949 1.3274 1.3601
1281.1655 1.6281 1.3243 1.587 1.3062 1.4013 1.4405 1.1905 1.4752 1.295 1.332 1.3595
1291.1666 1.6351 1.3262 1.5879 1.3076 1.402 1.4445 1.1907 1.4742 1.2948 1.3367 1.3584
1301.1679 1.6413 1.3274 1.5889 1.3089 1.4025 1.4475 1.1906 1.4725 1.2946 1.3416 1.3572
1311.169 1.6467 1.3285 1.5903 1.3099 1.4026 1.4506 1.1905 1.4713 1.2946 1.3464 1.3562
1321.1699 1.6531 1.33 1.5919 1.3115 1.4038 1.4546 1.1904 1.47 1.2945 1.3513 1.3553
1331.1707 1.6596 1.3321 1.5933 1.313 1.405 1.4594 1.1903 1.4688 1.2943 1.3556 1.3545
1341.1715 1.6671 1.3339 1.594 1.3145 1.406 1.4632 1.1898 1.4682 1.2939 1.3594 1.3535
1351.1724 1.675 1.3351 1.5944 1.3158 1.407 1.4676 1.1893 1.4674 1.2936 1.3633 1.352
1361.1732 1.6828 1.3361 1.5948 1.3176 1.4084 1.4721 1.1887 1.4667 1.2938 1.3674 1.3507
1371.174 1.6915 1.3375 1.596 1.3191 1.4096 1.4768 1.188 1.4666 1.2936 1.3706 1.3494
1381.1751 1.6998 1.3389 1.5984 1.3207 1.4106 1.4813 1.1871 1.4655 1.2933 1.374 1.3481
1391.1765 1.7094 1.3398 1.6006 1.3225 1.412 1.4861 1.1864 1.4646 1.2929 1.3775 1.3472
1401.178 1.717 1.3409 1.6021 1.3241 1.414 1.4909 1.1858 1.4639 1.2927 1.3809 1.3464
1411.1796 1.7231 1.342 1.6032 1.3255 1.4162 1.4963 1.1852 1.4634 1.2929 1.3854 1.3456
1421.1812 1.7304 1.3428 1.605 1.3273 1.4182 1.5023 1.1847 1.4627 1.2933 1.3897 1.3448
1431.1827 1.7361 1.3435 1.6063 1.329 1.4213 1.5087 1.1845 1.4621 1.2937 1.3939 1.3441
1441.1843 1.7435 1.3446 1.6087 1.3306 1.4244 1.5155 1.1844 1.4617 1.2943 1.398 1.3433
1451.1859 1.7494 1.3456 1.611 1.3322 1.4273 1.5207 1.1844 1.4614 1.2949 1.4023 1.3424
1461.1876 1.7564 1.3467 1.6134 1.3338 1.4307 1.5259 1.1843 1.4614 1.2955 1.4066 1.3413
1471.1892 1.7624 1.3477 1.6144 1.3356 1.4341 1.5308 1.1842 1.4614 1.2961 1.4104 1.3399
1481.1907 1.7695 1.3488 1.617 1.3376 1.4376 1.5353 1.1843 1.4614 1.2968 1.4141 1.3385
1491.1923 1.7777 1.3499 1.6187 1.3394 1.441 1.54 1.1845 1.4614 1.2973 1.4181 1.3369
1501.1941 1.7849 1.3512 1.6199 1.3412 1.4445 1.5451 1.1848 1.4618 1.298 1.4222 1.3353
1511.1958 1.792 1.3526 1.6203 1.3433 1.4476 1.55 1.1852 1.462 1.2989 1.4258 1.3339
1521.1973 1.7992 1.3538 1.6211 1.3456 1.4509 1.5544 1.1854 1.4625 1.2994 1.4291 1.3323
1531.1985 1.8081 1.3551 1.6233 1.3478 1.4537 1.558 1.1856 1.4626 1.2999 1.4322 1.3306
1541.1996 1.8155 1.3567 1.625 1.3501 1.4567 1.5612 1.1859 1.4626 1.3002 1.4344 1.329
1551.2006 1.8224 1.3584 1.6261 1.3528 1.4595 1.5647 1.1864 1.4625 1.3006 1.4357 1.3276
1561.2016 1.8293 1.3598 1.6268 1.3556 1.4626 1.5684 1.1868 1.4626 1.301 1.4374 1.3265
1571.2027 1.8373 1.3612 1.6292 1.3586 1.466 1.5719 1.1872 1.4625 1.3016 1.4383 1.3253
1581.2036 1.8457 1.363 1.6309 1.3618 1.4698 1.5751 1.1876 1.4623 1.3022 1.439 1.3241
1591.2047 1.8533 1.3647 1.6325 1.3647 1.4742 1.579 1.1878 1.462 1.303 1.4396 1.3228
1601.2057 1.8602 1.366 1.6333 1.3677 1.4784 1.5819 1.1881 1.4611 1.3035 1.4399 1.3214
1611.2064 1.8652 1.3671 1.632 1.3705 1.4824 1.5843 1.1881 1.4605 1.3037 1.4399 1.3202
1621.2074 1.8707 1.3692 1.6316 1.3734 1.4868 1.5861 1.1884 1.4604 1.3042 1.4403 1.3193
1631.2087 1.8767 1.3713 1.6316 1.3763 1.4914 1.5882 1.1885 1.4599 1.3046 1.4415 1.3183
1641.21 1.8816 1.373 1.6308 1.3791 1.4954 1.5906 1.1885 1.4596 1.3049 1.4417 1.3173
1651.2111 1.8875 1.3746 1.6309 1.3823 1.499 1.5926 1.1885 1.4598 1.3048 1.4423 1.316
1661.2122 1.8935 1.3761 1.6317 1.385 1.5028 1.595 1.1884 1.4597 1.3049 1.4427 1.3147
1671.2132 1.9 1.3774 1.6318 1.3882 1.5065 1.597 1.1881 1.4594 1.3051 1.4428 1.313
1681.2144 1.907 1.3788 1.6324 1.3919 1.5113 1.5987 1.1879 1.4588 1.3053 1.443 1.3114
1691.2158 1.9145 1.3805 1.6336 1.3955 1.5161 1.5995 1.1877 1.4583 1.3055 1.4423 1.31
1701.2174 1.9231 1.3819 1.6356 1.3991 1.5214 1.6006 1.1874 1.4581 1.3057 1.4417 1.3086
1711.2185 1.9321 1.383 1.6374 1.4026 1.5268 1.6017 1.1871 1.4576 1.3059 1.4398 1.3074
1721.2195 1.9408 1.3844 1.6395 1.4067 1.5326 1.6026 1.1868 1.4571 1.306 1.4374 1.3057
1731.2204 1.9479 1.3857 1.6414 1.4106 1.5378 1.6042 1.1865 1.4567 1.3062 1.4351 1.3043
1741.2212 1.954 1.3866 1.6433 1.4144 1.5432 1.6059 1.1862 1.4566 1.3064 1.4332 1.303
1751.222 1.9599 1.3875 1.6458 1.4187 1.5496 1.6082 1.186 1.4563 1.3069 1.4313 1.3016
1761.2228 1.9663 1.3884 1.6475 1.4225 1.5556 1.6095 1.1858 1.4556 1.3071 1.4306 1.3
1771.2236 1.9732 1.3902 1.6502 1.4267 1.5618 1.6113 1.1854 1.4552 1.3075 1.4296 1.2987
1781.2244 1.98 1.3919 1.6528 1.4312 1.5682 1.6128 1.185 1.4554 1.3078 1.4286 1.2971
1791.2252 1.9862 1.3935 1.6551 1.4355 1.5743 1.615 1.1847 1.4554 1.3079 1.4284 1.2958
1801.2259 1.9925 1.3953 1.6571 1.4397 1.5802 1.6167 1.1844 1.4554 1.3077 1.4282 1.2945
1811.2268 1.9977 1.3973 1.6592 1.4438 1.5862 1.6191 1.1845 1.4555 1.3074 1.4281 1.2937
1821.2277 2.0015 1.3992 1.6602 1.4483 1.592 1.6214 1.1846 1.4558 1.3074 1.4287 1.2931
1831.2289 2.0067 1.4008 1.6625 1.4531 1.5979 1.6229 1.1848 1.4557 1.3075 1.4299 1.2924
1841.23 2.0106 1.4024 1.6638 1.458 1.6041 1.6243 1.1852 1.4558 1.3078 1.4307 1.2917
1851.2311 2.0159 1.4042 1.6644 1.4633 1.6107 1.6253 1.1855 1.4559 1.3081 1.4314 1.2912
1861.2323 2.0199 1.4058 1.6649 1.4687 1.6173 1.6262 1.1859 1.4564 1.3084 1.4329 1.291
1871.2336 2.0257 1.4076 1.6665 1.474 1.6233 1.6275 1.1863 1.4566 1.3087 1.4343 1.2907
1881.2348 2.0316 1.4099 1.6675 1.479 1.629 1.6288 1.1869 1.4568 1.3092 1.4351 1.2904
1891.2358 2.0386 1.412 1.6686 1.4841 1.6353 1.6296 1.1873 1.4567 1.3095 1.4363 1.2901
1901.2366 2.0451 1.4142 1.6679 1.489 1.6413 1.631 1.1877 1.4569 1.3099 1.4377 1.2898
1911.2375 2.0524 1.4165 1.6689 1.4944 1.6471 1.6327 1.1884 1.4572 1.3103 1.4391 1.2896
1921.2382 2.0602 1.4195 1.6707 1.4997 1.653 1.6337 1.1892 1.4572 1.311 1.4407 1.2893
1931.239 2.0673 1.423 1.6727 1.5053 1.6589 1.6347 1.1898 1.4572 1.3116 1.4417 1.289
1941.2398 2.0763 1.4263 1.6754 1.5111 1.6643 1.6355 1.1905 1.4574 1.3123 1.4424 1.2886
1951.2406 2.0862 1.4293 1.6776 1.5166 1.6691 1.637 1.191 1.457 1.3129 1.4428 1.2882
1961.2411 2.0951 1.4328 1.6788 1.5219 1.6736 1.6383 1.1913 1.4571 1.3133 1.4434 1.2877
1971.2412 2.1029 1.4367 1.6792 1.5273 1.6779 1.6388 1.1918 1.4571 1.3138 1.4441 1.2872
1981.2412 2.1105 1.4407 1.6794 1.5326 1.6818 1.6397 1.1921 1.4574 1.3142 1.4449 1.2869
1991.2412 2.1193 1.4445 1.6796 1.5382 1.6861 1.6404 1.1924 1.4573 1.3146 1.446 1.2865
2001.2413 2.1283 1.4481 1.6806 1.5435 1.6899 1.6403 1.1927 1.457 1.3152 1.448 1.2861
2011.2416 2.138 1.4523 1.6824 1.5486 1.6936 1.6405 1.1929 1.4568 1.3157 1.4505 1.2859
2021.242 2.1473 1.457 1.6844 1.5541 1.698 1.6406 1.1932 1.4566 1.3163 1.4531 1.2855
2031.2424 2.1552 1.4612 1.6852 1.5596 1.7033 1.6413 1.1933 1.4566 1.3168 1.4554 1.2851
2041.2429 2.1646 1.465 1.6868 1.5654 1.7072 1.6416 1.1934 1.4563 1.3172 1.4578 1.2849
2051.2433 2.1748 1.4683 1.6881 1.5712 1.712 1.6415 1.1936 1.4564 1.3177 1.4604 1.2844
2061.2437 2.1856 1.4718 1.6894 1.5766 1.717 1.6414 1.1937 1.4563 1.3181 1.4625 1.284
2071.244 2.1974 1.4755 1.6912 1.5817 1.722 1.641 1.1941 1.4563 1.3186 1.4642 1.2835
2081.2444 2.2105 1.4788 1.693 1.5876 1.7271 1.6412 1.1944 1.4563 1.3189 1.4655 1.2831
2091.2447 2.2239 1.482 1.6954 1.5932 1.7319 1.6418 1.1946 1.4564 1.319 1.4665 1.283
2101.2449 2.2379 1.4844 1.6979 1.5991 1.7372 1.6429 1.1948 1.4565 1.3189 1.4681 1.2828
2111.2451 2.2515 1.4864 1.7006 1.6051 1.7426 1.6432 1.1953 1.4567 1.3187 1.4701 1.2826
2121.2452 2.2678 1.4889 1.7038 1.6108 1.7472 1.6437 1.1958 1.4568 1.3186 1.4722 1.2825
2131.2453 2.2852 1.4915 1.7077 1.6164 1.7523 1.6442 1.1964 1.457 1.3184 1.4742 1.2824
2141.2454 2.3031 1.4935 1.7113 1.6222 1.7574 1.6449 1.1971 1.4571 1.3181 1.4762 1.2824
2151.2453 2.32 1.4953 1.7149 1.6277 1.7619 1.6458 1.1979 1.4573 1.3177 1.4784 1.2823
2161.2454 2.335 1.4976 1.7189 1.6335 1.7676 1.6471 1.1988 1.4577 1.3173 1.4805 1.2825
2171.2456 2.35 1.5004 1.722 1.6395 1.7733 1.648 1.1998 1.458 1.317 1.4836 1.2825
2181.2459 2.364 1.5032 1.7248 1.6456 1.7787 1.6488 1.201 1.4587 1.3167 1.4869 1.2824
2191.2462 2.3766 1.5056 1.7271 1.6514 1.7846 1.6493 1.2023 1.4592 1.3164 1.4911 1.2823
2201.2465 2.3855 1.5073 1.7283 1.6566 1.7899 1.6495 1.2035 1.4596 1.3161 1.4956 1.2822
2211.2466 2.394 1.5084 1.7289 1.6615 1.7952 1.6495 1.2048 1.4602 1.3156 1.5001 1.2822
2221.2466 2.4037 1.5093 1.7297 1.6664 1.8008 1.6493 1.2059 1.4607 1.3151 1.5049 1.2822
2231.2467 2.4123 1.5104 1.7297 1.6714 1.8064 1.6493 1.2072 1.461 1.3147 1.5089 1.2823
2241.2468 2.422 1.5115 1.7297 1.6767 1.8122 1.6488 1.2085 1.4613 1.314 1.5128 1.2823
2251.2468 2.4317 1.512 1.7291 1.6816 1.8179 1.6479 1.2097 1.4618 1.3134 1.5163 1.2824
2261.2468 2.4412 1.5119 1.7283 1.6862 1.8235 1.6474 1.2109 1.462 1.3129 1.5197 1.2824
2271.2467 2.4505 1.5129 1.7273 1.6906 1.8296 1.6468 1.2122 1.4624 1.3125 1.5224 1.2824
2281.2467 2.4621 1.5138 1.7269 1.6945 1.8358 1.6463 1.2135 1.4624 1.312 1.5252 1.2824
2291.2467 2.473 1.5145 1.7271 1.6987 1.8424 1.6453 1.2148 1.4623 1.3115 1.5283 1.2824
2301.2465 2.4817 1.5151 1.7268 1.703 1.8492 1.6449 1.2161 1.4617 1.3109 1.5311 1.2825
2311.2464 2.4884 1.516 1.7257 1.707 1.8543 1.6442 1.2174 1.4613 1.3105 1.5339 1.2826
2321.2464 2.4951 1.5169 1.7253 1.7115 1.8594 1.6431 1.2186 1.461 1.3101 1.5373 1.2827
2331.2464 2.5002 1.5182 1.7243 1.7155 1.8645 1.6421 1.2197 1.4607 1.3098 1.5405 1.283
2341.2464 2.5037 1.5188 1.7233 1.7194 1.8682 1.641 1.2209 1.4605 1.3092 1.5433 1.2833
2351.2464 2.5064 1.519 1.7229 1.7226 1.8722 1.6391 1.2219 1.4603 1.3088 1.5461 1.2834
2361.2463 2.5092 1.52 1.7226 1.7252 1.8761 1.6376 1.2228 1.4602 1.3085 1.5489 1.2835
2371.2461 2.5129 1.5208 1.7222 1.7275 1.8814 1.6357 1.2236 1.4599 1.3081 1.5514 1.2836
2381.2458 2.5156 1.5213 1.7215 1.73 1.8868 1.6338 1.2245 1.4596 1.3074 1.5538 1.2837
2391.2456 2.5174 1.5218 1.7207 1.7317 1.8917 1.6316 1.2252 1.4589 1.3069 1.5558 1.2837
2401.2454 2.5184 1.5219 1.7203 1.7331 1.8968 1.6294 1.2259 1.4582 1.3063 1.5577 1.2837
2411.245 2.5191 1.5212 1.7199 1.7345 1.9016 1.6266 1.2266 1.4578 1.3056 1.5591 1.2838
2421.2447 2.5188 1.521 1.7191 1.7351 1.9058 1.6238 1.2273 1.4572 1.3051 1.5607 1.2838
2431.2444 2.5194 1.5213 1.7175 1.7353 1.9103 1.621 1.2281 1.4566 1.3046 1.5619 1.2837
2441.244 2.5179 1.5214 1.7161 1.7356 1.9146 1.6185 1.2291 1.4561 1.3041 1.563 1.2835
2451.2435 2.5148 1.5206 1.7137 1.7354 1.9194 1.6163 1.2302 1.4554 1.3036 1.564 1.2834
2461.243 2.5117 1.5198 1.7109 1.7355 1.9255 1.6142 1.2313 1.4547 1.303 1.5645 1.2832
2471.2427 2.5114 1.5197 1.709 1.7347 1.9311 1.6115 1.2323 1.4541 1.3023 1.5644 1.2829
2481.2423 2.5099 1.5198 1.707 1.7337 1.9359 1.6092 1.2332 1.4535 1.3017 1.5643 1.2825
2491.2421 2.5081 1.5196 1.7056 1.7332 1.9402 1.6066 1.2343 1.4528 1.301 1.5641 1.2819
2501.242 2.5052 1.5194 1.7042 1.7324 1.9449 1.6046 1.2356 1.4521 1.3003 1.5635 1.2815
Data for figure immediately follows

Data for Appendix 4 - Long Memory Hypothesis Tests: Commodity (Silver - Sugar)

xiSilverCattleCocoaCoffeeCornCottonRubberSoybeansSugarWheat
00.9683 1.5446 2.0956 1.653 0.9823 2.055 0.6766 0.8807 1.2471 1.4085
11.0113 1.5769 1.7559 1.6539 1.0604 2.0834 0.695 0.903 1.2549 1.4952
21.0297 1.605 1.5896 1.6323 1.1137 2.0555 0.7306 0.9034 1.2671 1.5522
31.0236 1.6347 1.4914 1.6231 1.1508 2.032 0.742 0.911 1.2659 1.5694
41.0176 1.6361 1.4306 1.604 1.1829 1.9759 0.7304 0.9188 1.2778 1.5801
51.0127 1.6235 1.3873 1.5977 1.2134 1.948 0.7096 0.9231 1.2752 1.5671
61.0168 1.6234 1.354 1.5899 1.2521 1.9292 0.708 0.9267 1.2799 1.571
71.02 1.6166 1.3241 1.5896 1.2839 1.9146 0.7168 0.933 1.2882 1.5742
81.0229 1.616 1.2967 1.5911 1.2975 1.8967 0.7313 0.9414 1.2973 1.5698
91.0231 1.5994 1.272 1.5912 1.3066 1.877 0.7487 0.9487 1.3071 1.5595
101.0226 1.5925 1.2496 1.589 1.3269 1.8549 0.7641 0.9568 1.3124 1.5602
111.0252 1.5852 1.2316 1.5854 1.3409 1.8398 0.7824 0.9672 1.3217 1.5648
121.0255 1.5785 1.2153 1.584 1.3513 1.8241 0.8017 0.9793 1.3297 1.5675
131.0307 1.5786 1.2011 1.5818 1.3574 1.8077 0.8259 0.9909 1.3337 1.5733
141.0311 1.576 1.1885 1.5814 1.3609 1.7946 0.848 0.9996 1.3401 1.5762
151.0314 1.5672 1.1767 1.5731 1.3627 1.7837 0.8622 1.0076 1.3427 1.5847
161.0329 1.5589 1.1654 1.5642 1.3661 1.7738 0.8735 1.0146 1.3469 1.5844
171.0322 1.5519 1.1552 1.5572 1.3693 1.7636 0.8797 1.0238 1.3538 1.5815
181.033 1.5482 1.1468 1.5493 1.3759 1.7553 0.8895 1.0343 1.3584 1.5782
191.0313 1.5467 1.1403 1.5396 1.3837 1.7492 0.8961 1.0402 1.3625 1.5734
201.0313 1.5408 1.1354 1.5287 1.3912 1.7431 0.8946 1.0432 1.365 1.5675
211.0309 1.5383 1.1317 1.5172 1.4033 1.7369 0.8912 1.0462 1.365 1.5615
221.0329 1.5397 1.1288 1.5074 1.416 1.7307 0.8907 1.0542 1.3686 1.5566
231.0365 1.5433 1.1269 1.501 1.429 1.7268 0.8902 1.0571 1.3744 1.5524
241.0385 1.5441 1.1258 1.4954 1.4378 1.7234 0.8883 1.0623 1.3778 1.5498
251.0435 1.5427 1.1247 1.4902 1.4438 1.7211 0.887 1.0686 1.3783 1.5462
261.0475 1.5399 1.1244 1.4843 1.4514 1.7202 0.8893 1.0741 1.3788 1.5425
271.0512 1.5408 1.1249 1.4788 1.4632 1.7207 0.8916 1.0773 1.3785 1.5399
281.0568 1.5462 1.1257 1.4735 1.4744 1.7218 0.8945 1.081 1.3806 1.5395
291.0619 1.5493 1.1265 1.4688 1.4791 1.7216 0.8999 1.0818 1.3813 1.5356
301.0687 1.5549 1.1271 1.4639 1.4845 1.7209 0.9067 1.083 1.3832 1.5335
311.0751 1.56 1.1277 1.4594 1.4903 1.719 0.9127 1.0845 1.3863 1.5312
321.0831 1.5672 1.1284 1.4555 1.4925 1.7169 0.9177 1.0856 1.3915 1.5273
331.09 1.5753 1.1291 1.4514 1.4956 1.7132 0.9241 1.0851 1.3961 1.5243
341.0992 1.5818 1.1302 1.4471 1.5026 1.7092 0.9294 1.0857 1.4001 1.521
351.1071 1.588 1.1315 1.4436 1.5074 1.7027 0.9295 1.0857 1.4028 1.5193
361.1141 1.5934 1.133 1.4391 1.5108 1.6966 0.9256 1.0876 1.4062 1.5142
371.1225 1.6001 1.1345 1.4347 1.5163 1.6897 0.922 1.0885 1.4102 1.5115
381.1288 1.6072 1.1356 1.43 1.5198 1.6826 0.9181 1.0893 1.4157 1.5079
391.1352 1.6132 1.1366 1.4242 1.5226 1.6756 0.9151 1.0887 1.4204 1.504
401.1399 1.6181 1.1374 1.4185 1.5261 1.668 0.9082 1.0902 1.4235 1.5008
411.1464 1.6211 1.138 1.4135 1.5273 1.6596 0.9 1.0922 1.4274 1.4981
421.1502 1.6248 1.1388 1.4089 1.5291 1.6517 0.896 1.0953 1.433 1.4962
431.1531 1.63 1.1395 1.4056 1.5285 1.6437 0.8924 1.0984 1.4396 1.4943
441.1566 1.6371 1.1403 1.4037 1.5316 1.6356 0.8907 1.1014 1.4452 1.4914
451.1604 1.6449 1.1408 1.4023 1.5347 1.6277 0.8885 1.105 1.4502 1.4893
461.164 1.6504 1.1409 1.4006 1.54 1.6199 0.8862 1.11 1.4546 1.487
471.1671 1.6554 1.1409 1.3993 1.5458 1.6119 0.8865 1.1161 1.4583 1.4854
481.1697 1.6616 1.1409 1.397 1.5484 1.6037 0.8883 1.1226 1.4611 1.4827
491.1739 1.6669 1.1409 1.3941 1.5507 1.5945 0.8902 1.1273 1.4637 1.4799
501.1787 1.6712 1.1411 1.3916 1.5528 1.5865 0.8923 1.1313 1.4636 1.477
511.1843 1.675 1.1414 1.3888 1.556 1.5777 0.8937 1.1365 1.4649 1.4738
521.1904 1.6807 1.1413 1.3853 1.559 1.5696 0.8962 1.1405 1.4663 1.4702
531.1954 1.6863 1.141 1.3821 1.5621 1.5621 0.8989 1.1438 1.4681 1.4668
541.201 1.6913 1.1402 1.3788 1.565 1.555 0.9017 1.147 1.4707 1.4625
551.2052 1.6966 1.1391 1.3762 1.5678 1.5484 0.9028 1.1494 1.4717 1.4583
561.2092 1.701 1.138 1.3736 1.5717 1.5421 0.9037 1.1506 1.4725 1.4537
571.2128 1.7063 1.137 1.3708 1.5761 1.5358 0.9049 1.1508 1.472 1.4492
581.218 1.7113 1.1359 1.3681 1.5801 1.5302 0.9063 1.1512 1.4724 1.446
591.2217 1.7172 1.1346 1.3655 1.5822 1.5247 0.9088 1.1523 1.4728 1.4436
601.2263 1.7228 1.1332 1.3626 1.5864 1.5197 0.9102 1.1528 1.4712 1.4409
611.231 1.7284 1.1317 1.3599 1.5908 1.5154 0.9114 1.1537 1.4702 1.4378
621.235 1.734 1.1301 1.3577 1.5954 1.5114 0.9128 1.154 1.4685 1.4352
631.238 1.7395 1.1283 1.3561 1.6006 1.5081 0.9161 1.1558 1.466 1.4331
641.2405 1.7441 1.1269 1.3546 1.6046 1.5051 0.9198 1.1582 1.4623 1.4325
651.2433 1.7475 1.1256 1.3535 1.6079 1.5023 0.9251 1.16 1.4582 1.4307
661.2446 1.7503 1.1247 1.3523 1.6103 1.4989 0.9306 1.1624 1.4539 1.4295
671.2453 1.7543 1.124 1.3505 1.613 1.4962 0.9348 1.164 1.4483 1.4287
681.2461 1.7593 1.1232 1.3484 1.6158 1.494 0.9407 1.1654 1.4437 1.4269
691.2454 1.7643 1.1224 1.3459 1.6192 1.4918 0.9484 1.1678 1.4395 1.4242
701.242 1.7698 1.1215 1.3431 1.6234 1.4893 0.954 1.1696 1.4348 1.4213
711.239 1.7743 1.1207 1.3404 1.6264 1.4869 0.9574 1.1706 1.4303 1.418
721.2369 1.7782 1.1199 1.3377 1.6304 1.4842 0.9592 1.1717 1.425 1.4142
731.2348 1.7814 1.1195 1.335 1.6325 1.4813 0.9616 1.1719 1.4205 1.4099
741.2336 1.7854 1.1194 1.3324 1.6341 1.478 0.9638 1.1727 1.4167 1.4065
751.2311 1.7876 1.1195 1.3297 1.6384 1.475 0.9649 1.1728 1.4115 1.4031
761.2279 1.7885 1.1198 1.3265 1.6424 1.4718 0.9636 1.1717 1.408 1.4
771.226 1.7893 1.1201 1.3239 1.6446 1.4686 0.9627 1.1702 1.4052 1.3971
781.2231 1.7906 1.1206 1.3212 1.6437 1.465 0.964 1.1681 1.403 1.3946
791.2207 1.7915 1.1211 1.3187 1.6428 1.4619 0.966 1.1671 1.4012 1.3918
801.2172 1.7915 1.1216 1.3161 1.6409 1.4588 0.9682 1.1656 1.3999 1.3895
811.2129 1.7917 1.1223 1.3135 1.6385 1.4557 0.97 1.164 1.3984 1.3876
821.209 1.7926 1.1231 1.3109 1.6367 1.4526 0.9727 1.1622 1.3974 1.3852
831.2042 1.7924 1.1241 1.3088 1.6356 1.4494 0.9762 1.1603 1.3976 1.3827
841.1982 1.7917 1.125 1.307 1.6319 1.4466 0.981 1.159 1.3975 1.3798
851.1922 1.7898 1.1259 1.3045 1.6306 1.4439 0.9859 1.1574 1.3966 1.3778
861.1866 1.7883 1.1269 1.3022 1.6289 1.4409 0.9896 1.1558 1.3956 1.3753
871.1812 1.7862 1.1278 1.3001 1.6279 1.4378 0.9937 1.1551 1.3931 1.373
881.1761 1.7838 1.1288 1.2979 1.6275 1.4347 0.9991 1.1528 1.3916 1.3707
891.1714 1.7818 1.1299 1.2962 1.6274 1.4316 1.0051 1.1504 1.3901 1.368
901.1662 1.7809 1.1311 1.2946 1.6279 1.429 1.0109 1.1483 1.3881 1.366
911.1616 1.7791 1.1325 1.2928 1.6278 1.4263 1.0157 1.1463 1.3865 1.3634
921.1577 1.7757 1.1337 1.2914 1.6268 1.424 1.0209 1.1453 1.3851 1.3606
931.155 1.7733 1.1348 1.2905 1.6263 1.4219 1.0268 1.1439 1.3839 1.3584
941.1521 1.7704 1.1359 1.29 1.6269 1.4199 1.0327 1.142 1.3832 1.3563
951.1495 1.768 1.1369 1.2897 1.6266 1.4177 1.0379 1.1403 1.3837 1.3545
961.1474 1.7656 1.1382 1.2892 1.6272 1.4155 1.0417 1.1384 1.3834 1.3528
971.1452 1.7626 1.1394 1.2887 1.6281 1.4137 1.0453 1.1368 1.3835 1.3518
981.1445 1.7601 1.1408 1.2882 1.6281 1.4117 1.0502 1.1353 1.3841 1.3505
991.1432 1.7588 1.1422 1.2876 1.6266 1.4097 1.0546 1.134 1.385 1.3499
1001.1422 1.7572 1.1436 1.287 1.6243 1.4078 1.0595 1.1323 1.3853 1.3485
1011.1414 1.7556 1.145 1.2863 1.6232 1.4059 1.0639 1.1309 1.3862 1.3471
1021.1406 1.7546 1.1464 1.2855 1.6217 1.4041 1.0689 1.129 1.3873 1.3464
1031.1401 1.7537 1.1478 1.285 1.6192 1.4025 1.0748 1.128 1.389 1.3454
1041.1396 1.7528 1.1492 1.2844 1.6168 1.4011 1.0815 1.1268 1.3911 1.3444
1051.139 1.7528 1.1506 1.2836 1.6162 1.3998 1.0879 1.1263 1.3932 1.3434
1061.139 1.7536 1.152 1.2828 1.6142 1.3986 1.0942 1.1263 1.3952 1.3427
1071.1397 1.7554 1.1533 1.2823 1.6108 1.3975 1.1009 1.1275 1.3974 1.3419
1081.1395 1.7579 1.1545 1.2821 1.6081 1.3965 1.1076 1.1279 1.4006 1.3408
1091.139 1.7603 1.1556 1.2819 1.604 1.3953 1.1145 1.1282 1.4045 1.3396
1101.1391 1.7629 1.1568 1.2818 1.5992 1.3942 1.1194 1.1285 1.4082 1.3387
1111.1391 1.7656 1.1579 1.2817 1.5957 1.393 1.1237 1.1292 1.4106 1.338
1121.139 1.7671 1.159 1.2815 1.5921 1.3921 1.127 1.1296 1.4122 1.3371
1131.1389 1.7684 1.1601 1.2817 1.5884 1.3912 1.1303 1.13 1.4139 1.3368
1141.1384 1.7705 1.161 1.282 1.5857 1.3906 1.1344 1.1302 1.415 1.3365
1151.1384 1.7733 1.1619 1.2823 1.5829 1.3899 1.1379 1.1298 1.4165 1.3362
1161.1385 1.7757 1.1629 1.2828 1.5803 1.3896 1.1413 1.1298 1.4182 1.336
1171.1386 1.7778 1.164 1.2835 1.5779 1.3891 1.1444 1.1301 1.42 1.3359
1181.139 1.779 1.1652 1.2843 1.5762 1.3885 1.1479 1.1318 1.4222 1.3357
1191.1397 1.7811 1.1666 1.2851 1.575 1.3879 1.1527 1.1332 1.4238 1.3354
1201.1409 1.7826 1.1679 1.2859 1.5745 1.3874 1.1577 1.1348 1.4255 1.3349
1211.1421 1.7843 1.1695 1.2867 1.5725 1.3871 1.1615 1.1359 1.427 1.3345
1221.143 1.7854 1.1711 1.2875 1.5713 1.3866 1.1648 1.1366 1.428 1.3339
1231.1434 1.7863 1.1729 1.2885 1.5696 1.3861 1.1696 1.1369 1.4293 1.3331
1241.1435 1.7872 1.1748 1.2895 1.5671 1.3857 1.1749 1.1371 1.4303 1.3322
1251.1438 1.7883 1.1766 1.2904 1.5651 1.3853 1.1795 1.1372 1.4306 1.3314
1261.1438 1.7892 1.1784 1.2916 1.5636 1.3849 1.1841 1.1377 1.4314 1.3306
1271.1436 1.7896 1.1802 1.2925 1.5612 1.3847 1.1885 1.138 1.4318 1.3297
1281.1438 1.7906 1.1821 1.2936 1.559 1.3845 1.1929 1.1386 1.4328 1.3289
1291.1436 1.7912 1.1842 1.2946 1.5567 1.3842 1.1971 1.139 1.4331 1.3285
1301.1434 1.7916 1.1863 1.2959 1.5543 1.3841 1.2027 1.1393 1.4328 1.3278
1311.1434 1.7914 1.1885 1.297 1.5522 1.384 1.2081 1.1391 1.4332 1.3272
1321.1436 1.7915 1.1908 1.2983 1.5496 1.3838 1.2119 1.1391 1.4342 1.3268
1331.1439 1.7908 1.1933 1.2997 1.5479 1.3836 1.2161 1.1394 1.4355 1.3264
1341.1442 1.79 1.1959 1.301 1.5461 1.3834 1.2205 1.1405 1.437 1.3263
1351.1447 1.7898 1.1986 1.3023 1.5441 1.383 1.2261 1.1401 1.4388 1.3262
1361.1458 1.7893 1.2015 1.3037 1.5426 1.3826 1.2306 1.1403 1.4414 1.3263
1371.1465 1.7883 1.2046 1.3047 1.5406 1.3823 1.2336 1.1409 1.4434 1.3264
1381.147 1.7872 1.2078 1.3059 1.5387 1.382 1.2383 1.1419 1.4454 1.3267
1391.1479 1.7864 1.2111 1.3071 1.5369 1.3818 1.2434 1.1423 1.4479 1.3267
1401.1487 1.7854 1.2144 1.3084 1.5347 1.3817 1.2486 1.1433 1.4509 1.3267
1411.1498 1.7844 1.2177 1.3098 1.5319 1.3816 1.254 1.1437 1.4533 1.3271
1421.1511 1.7828 1.2209 1.3112 1.5293 1.3815 1.2594 1.1437 1.456 1.3275
1431.1522 1.7818 1.224 1.3127 1.528 1.3814 1.2642 1.1439 1.4589 1.3279
1441.1533 1.7812 1.2271 1.314 1.5269 1.3814 1.2692 1.144 1.4618 1.3284
1451.1543 1.7809 1.23 1.3154 1.526 1.3812 1.2725 1.144 1.4641 1.3287
1461.1553 1.7805 1.2327 1.3165 1.5251 1.3811 1.275 1.1445 1.4666 1.3292
1471.1561 1.7797 1.2353 1.3178 1.5246 1.3812 1.2778 1.1452 1.4693 1.3295
1481.1565 1.7791 1.2378 1.319 1.5237 1.3813 1.2806 1.1459 1.4723 1.33
1491.1573 1.7783 1.2403 1.3204 1.5236 1.3815 1.2822 1.1469 1.4755 1.3304
1501.158 1.7771 1.2426 1.3215 1.524 1.3816 1.2831 1.147 1.4785 1.3305
1511.1586 1.7757 1.2449 1.3227 1.5248 1.3818 1.2844 1.147 1.4813 1.3308
1521.1588 1.7743 1.2472 1.324 1.5267 1.3821 1.2858 1.1469 1.4845 1.3309
1531.1588 1.773 1.2494 1.3253 1.5281 1.3824 1.2868 1.1472 1.4881 1.3311
1541.1587 1.7716 1.2517 1.3264 1.5293 1.3828 1.2885 1.148 1.4913 1.3309
1551.1583 1.7708 1.2537 1.3276 1.5303 1.3833 1.2899 1.1491 1.4948 1.3308
1561.158 1.7694 1.2557 1.3288 1.5306 1.3837 1.2916 1.1503 1.4984 1.3307
1571.1578 1.7679 1.2576 1.3299 1.5304 1.3843 1.2925 1.1512 1.5018 1.3305
1581.1575 1.7658 1.2593 1.3311 1.5303 1.3848 1.2943 1.1509 1.5054 1.3307
1591.1571 1.7638 1.2608 1.3323 1.53 1.3854 1.296 1.1509 1.5084 1.3306
1601.1565 1.762 1.2622 1.3333 1.5293 1.386 1.2969 1.1499 1.5116 1.3307
1611.1554 1.7604 1.2635 1.3343 1.5289 1.3865 1.2981 1.1491 1.5153 1.3306
1621.1548 1.7593 1.2648 1.3354 1.5289 1.3874 1.2995 1.148 1.5188 1.3307
1631.1547 1.7575 1.266 1.3365 1.5288 1.3882 1.3007 1.1472 1.5224 1.3308
1641.1541 1.7552 1.2672 1.3376 1.5288 1.3893 1.303 1.1458 1.5258 1.3311
1651.1538 1.753 1.2683 1.339 1.5288 1.3902 1.3053 1.1442 1.5297 1.3316
1661.1536 1.7509 1.2693 1.3401 1.5279 1.3911 1.3068 1.1429 1.5339 1.3323
1671.1531 1.7489 1.2702 1.3414 1.5271 1.3919 1.3091 1.142 1.5381 1.333
1681.1528 1.7468 1.2711 1.3428 1.526 1.3929 1.3112 1.1412 1.5422 1.3336
1691.152 1.7445 1.2721 1.3444 1.5244 1.3938 1.3137 1.1408 1.5459 1.3343
1701.1515 1.7419 1.2731 1.3458 1.5221 1.3948 1.3153 1.1402 1.5506 1.335
1711.1508 1.7397 1.2742 1.3473 1.5199 1.3957 1.3166 1.14 1.5549 1.3354
1721.1503 1.7371 1.2752 1.3486 1.5177 1.3965 1.3171 1.1396 1.559 1.3359
1731.1502 1.7349 1.2763 1.3498 1.5148 1.3972 1.3188 1.1395 1.5635 1.3364
1741.1503 1.7327 1.2774 1.3512 1.5132 1.398 1.32 1.1393 1.5673 1.3367
1751.1506 1.7302 1.2785 1.3528 1.5111 1.3985 1.3207 1.1393 1.5709 1.337
1761.1512 1.7274 1.2795 1.3541 1.5088 1.399 1.3219 1.139 1.5749 1.3374
1771.1518 1.7248 1.2804 1.3555 1.5058 1.3997 1.3227 1.1393 1.5783 1.3376
1781.1525 1.722 1.2814 1.3568 1.5031 1.4003 1.3237 1.1399 1.5813 1.3379
1791.1534 1.7195 1.2824 1.3583 1.5004 1.401 1.3248 1.1405 1.5843 1.3384
1801.1539 1.7173 1.2834 1.3598 1.4977 1.4018 1.3252 1.1407 1.5879 1.339
1811.1546 1.7148 1.2844 1.3612 1.495 1.4025 1.3262 1.1408 1.5907 1.3396
1821.156 1.7126 1.2856 1.3628 1.4926 1.4031 1.3262 1.1412 1.5935 1.3403
1831.1575 1.7102 1.2866 1.3645 1.4904 1.4038 1.3271 1.1418 1.5964 1.3407
1841.1587 1.7081 1.2876 1.3663 1.4878 1.4044 1.3287 1.1423 1.5986 1.3419
1851.1599 1.7068 1.2885 1.368 1.4852 1.4048 1.3282 1.1426 1.6007 1.343
1861.1615 1.7058 1.2893 1.37 1.4826 1.4054 1.327 1.1431 1.6025 1.3441
1871.1629 1.7047 1.2901 1.3718 1.4803 1.406 1.3268 1.1438 1.6043 1.3454
1881.164 1.7031 1.2908 1.3738 1.478 1.4067 1.3263 1.1445 1.6063 1.3465
1891.1652 1.7016 1.2917 1.3757 1.4762 1.4074 1.3255 1.1449 1.6084 1.3478
1901.1668 1.7002 1.2925 1.3777 1.4751 1.408 1.3241 1.1451 1.6112 1.3493
1911.1683 1.6993 1.2934 1.3797 1.4734 1.4087 1.3229 1.1452 1.6137 1.3504
1921.1697 1.6985 1.2944 1.3816 1.4716 1.4094 1.3219 1.1454 1.6165 1.3516
1931.1707 1.698 1.2953 1.3835 1.4697 1.4101 1.3216 1.1457 1.6194 1.3529
1941.1717 1.6983 1.2963 1.3853 1.4681 1.4108 1.3212 1.1464 1.6218 1.3541
1951.1726 1.6983 1.2972 1.3871 1.4669 1.4118 1.3206 1.1471 1.6252 1.3555
1961.1736 1.6984 1.2981 1.3888 1.4656 1.4128 1.3199 1.1481 1.6277 1.3569
1971.1743 1.6981 1.2992 1.3905 1.4644 1.414 1.3194 1.1485 1.63 1.3582
1981.175 1.6978 1.3002 1.3921 1.4633 1.4153 1.318 1.1492 1.6326 1.3596
1991.1756 1.6976 1.3013 1.3936 1.4624 1.4165 1.3176 1.1497 1.6352 1.3609
2001.1766 1.6978 1.3023 1.3952 1.4614 1.4178 1.316 1.1504 1.6376 1.3621
2011.1779 1.6979 1.3033 1.3968 1.4604 1.4191 1.3157 1.1509 1.6401 1.3635
2021.1792 1.6981 1.3043 1.3984 1.4589 1.4206 1.3152 1.1515 1.6424 1.3648
2031.1803 1.6985 1.3055 1.4001 1.4576 1.422 1.3133 1.152 1.645 1.3661
2041.1814 1.6986 1.3068 1.4019 1.4558 1.4233 1.3121 1.1528 1.6469 1.3676
2051.1825 1.6988 1.3081 1.4035 1.4543 1.4247 1.3123 1.1535 1.6488 1.3693
2061.1834 1.6992 1.3095 1.4051 1.4525 1.426 1.3121 1.1543 1.6509 1.3709
2071.1841 1.6993 1.3108 1.4065 1.4507 1.4274 1.3111 1.1552 1.6529 1.3725
2081.1848 1.6999 1.3122 1.4079 1.4484 1.4288 1.3105 1.1561 1.6549 1.3743
2091.1853 1.7006 1.3135 1.4092 1.4462 1.4304 1.3107 1.1571 1.6562 1.3762
2101.1861 1.7015 1.3149 1.4106 1.4442 1.4319 1.3114 1.1579 1.6572 1.3779
2111.187 1.7023 1.3163 1.4118 1.4423 1.4334 1.3117 1.1591 1.6587 1.3797
2121.1878 1.7029 1.3176 1.4129 1.44 1.4349 1.3119 1.1601 1.6597 1.3813
2131.1886 1.7031 1.3191 1.4138 1.4378 1.4365 1.313 1.1608 1.6613 1.3829
2141.1894 1.7032 1.3205 1.4149 1.4361 1.4381 1.3143 1.1617 1.6629 1.3845
2151.1903 1.703 1.3219 1.416 1.4339 1.4398 1.3155 1.1624 1.6646 1.3858
2161.1912 1.7031 1.3233 1.4174 1.4324 1.4414 1.3164 1.1627 1.6665 1.3874
2171.1924 1.7032 1.3246 1.4187 1.4308 1.4432 1.3176 1.163 1.6683 1.3889
2181.1938 1.7034 1.326 1.4201 1.4294 1.4447 1.3186 1.1629 1.6706 1.3906
2191.1955 1.7036 1.3274 1.4216 1.4282 1.4463 1.319 1.1626 1.6732 1.3923
2201.1972 1.7039 1.3288 1.4231 1.4266 1.4478 1.3191 1.1626 1.6755 1.394
2211.1989 1.7039 1.3302 1.4245 1.4253 1.4493 1.3185 1.1627 1.6779 1.3956
2221.2006 1.7035 1.3316 1.4258 1.4237 1.4508 1.3181 1.1632 1.6795 1.3973
2231.202 1.7027 1.333 1.4271 1.4224 1.4524 1.3174 1.1633 1.6814 1.3993
2241.2031 1.7018 1.3344 1.4282 1.4213 1.454 1.3163 1.1634 1.683 1.4013
2251.2044 1.7013 1.3359 1.4292 1.4203 1.4557 1.3155 1.1637 1.684 1.4034
2261.2057 1.7009 1.3373 1.43 1.4195 1.4573 1.315 1.1643 1.6854 1.4054
2271.2071 1.7001 1.3389 1.4308 1.4187 1.4589 1.3145 1.1651 1.6871 1.4076
2281.2085 1.6993 1.3404 1.4316 1.4183 1.4605 1.3144 1.1661 1.6885 1.4099
2291.2101 1.6984 1.3421 1.4324 1.418 1.4622 1.3152 1.1671 1.6893 1.4122
2301.2115 1.6974 1.3438 1.4331 1.4177 1.4639 1.3155 1.1678 1.6902 1.4148
2311.2127 1.6962 1.3455 1.4339 1.4175 1.4656 1.3158 1.1687 1.6909 1.417
2321.2143 1.6955 1.3472 1.4346 1.4169 1.4672 1.3163 1.1697 1.6915 1.4194
2331.2155 1.6945 1.3488 1.4353 1.4163 1.4688 1.3165 1.1704 1.6921 1.4217
2341.2167 1.6936 1.3505 1.4361 1.4155 1.4704 1.3172 1.1714 1.6925 1.424
2351.2178 1.6927 1.3522 1.4368 1.4147 1.472 1.3169 1.1724 1.6929 1.4263
2361.2188 1.6919 1.3539 1.4375 1.4139 1.4737 1.3163 1.1732 1.6927 1.4286
2371.2198 1.6912 1.3557 1.4382 1.4135 1.4753 1.3165 1.174 1.6922 1.431
2381.2206 1.6902 1.3574 1.4389 1.4128 1.4769 1.3161 1.1747 1.6918 1.4334
2391.2213 1.6892 1.3592 1.4397 1.4123 1.4784 1.3158 1.175 1.6917 1.4357
2401.222 1.6883 1.3609 1.4404 1.4115 1.4798 1.3159 1.1756 1.692 1.4381
2411.2225 1.6876 1.3627 1.4411 1.4104 1.4813 1.3154 1.1759 1.6914 1.4404
2421.2231 1.6869 1.3643 1.4417 1.4095 1.4827 1.3149 1.1763 1.6908 1.4426
2431.2234 1.686 1.366 1.4425 1.4083 1.4841 1.3149 1.1764 1.6905 1.4444
2441.224 1.6851 1.3676 1.4432 1.4066 1.4857 1.3153 1.1766 1.6899 1.4465
2451.2245 1.6841 1.3691 1.4438 1.405 1.4871 1.3164 1.1765 1.6893 1.4486
2461.2249 1.6833 1.3707 1.4445 1.4033 1.4885 1.3172 1.1765 1.6887 1.451
2471.225 1.6824 1.3722 1.4451 1.4017 1.4897 1.3176 1.1766 1.6884 1.4532
2481.2251 1.6813 1.3737 1.4455 1.4005 1.491 1.3191 1.1769 1.6882 1.4552
2491.2252 1.6804 1.3753 1.4459 1.3991 1.4921 1.3199 1.1775 1.6877 1.4575
2501.2251 1.6797 1.377 1.4463 1.3975 1.4932 1.3204 1.1783 1.6869 1.4599

Data for figure immediately follows

Data for Appendix 4 - Long Memory Hypothesis Tests: USD Bilateral Exchange Rate (Argentina - Russia)

xiArgentinaBrazilChileColombiaMexicoPeruIndonesiaIndiaSouth KoreaMalaysiaPhilippinesRussia
01.7481 1.9373 1.9016 1.907 0.9959 1.4364 1.5296 1.9405 1.9227 1.3735 1.4463 1.8629
11.7948 1.884 1.8467 1.906 0.994 1.3892 1.4331 2.0674 1.8242 1.3487 1.5269 1.7028
21.9163 1.8911 1.8746 1.9002 1.0018 1.423 1.4105 2.0619 1.7961 1.3527 1.6008 1.7267
32 1.8955 1.8753 1.8945 1.0101 1.4295 1.4211 2.0637 1.7932 1.3583 1.6178 1.855
42.0192 1.8748 1.8599 1.8688 1.0174 1.4366 1.4352 2.0732 1.8299 1.3455 1.6513 1.9647
52.0552 1.8728 1.8397 1.8671 1.0179 1.4418 1.4444 2.0855 1.8879 1.336 1.6859 1.9946
62.106 1.8662 1.8287 1.854 1.0271 1.4455 1.4578 2.0969 1.9318 1.3408 1.7163 1.9902
72.1206 1.8628 1.8209 1.8438 1.0385 1.4487 1.4671 2.1106 1.9474 1.3495 1.7505 1.9942
82.1263 1.867 1.8071 1.8369 1.0467 1.445 1.4656 2.1198 1.9393 1.3525 1.7678 1.9992
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1711.3902 1.6177 1.4392 1.4209 1.195 1.8527 1.2771 1.7695 1.5246 1.385 1.4648 1.5367
1721.3905 1.6181 1.4391 1.42 1.1945 1.8555 1.2764 1.7687 1.5257 1.3897 1.4639 1.5354
1731.3908 1.6182 1.4389 1.4193 1.1937 1.8576 1.2756 1.768 1.5267 1.3943 1.463 1.5338
1741.391 1.6181 1.4387 1.4185 1.1929 1.8592 1.2747 1.7669 1.5276 1.3988 1.462 1.5321
1751.3911 1.6181 1.4385 1.4176 1.1919 1.8609 1.2737 1.7655 1.5284 1.4033 1.461 1.5303
1761.3913 1.6184 1.4384 1.4167 1.1907 1.8621 1.2727 1.764 1.5292 1.4078 1.46 1.5287
1771.3916 1.6187 1.4385 1.4158 1.19 1.8634 1.2721 1.7624 1.5301 1.4127 1.459 1.5271
1781.3919 1.6188 1.4386 1.4149 1.1894 1.8653 1.2713 1.7608 1.5309 1.417 1.4581 1.5257
1791.3922 1.6191 1.4388 1.4141 1.189 1.8672 1.2703 1.7593 1.5317 1.4216 1.457 1.5242
1801.3924 1.6195 1.4387 1.4133 1.1886 1.8693 1.2691 1.7578 1.5322 1.4263 1.456 1.5229
1811.3926 1.6198 1.4386 1.4126 1.1884 1.8714 1.2677 1.7563 1.5329 1.4309 1.4551 1.5214
1821.393 1.6202 1.4386 1.4119 1.1881 1.8739 1.2663 1.7549 1.5335 1.4356 1.4543 1.5201
1831.3936 1.6207 1.4386 1.4112 1.188 1.8752 1.265 1.7534 1.5341 1.4404 1.4534 1.5186
1841.3941 1.621 1.4384 1.4104 1.1873 1.8767 1.2638 1.752 1.5346 1.4452 1.4525 1.5171
1851.3946 1.6213 1.4384 1.4097 1.1864 1.8791 1.2626 1.7505 1.5351 1.4498 1.4517 1.5156
1861.395 1.6217 1.4383 1.4091 1.1855 1.8819 1.2613 1.749 1.5356 1.454 1.4508 1.5143
1871.3955 1.6221 1.4381 1.4084 1.1848 1.8849 1.26 1.7474 1.536 1.4582 1.4499 1.5129
1881.3959 1.6224 1.4378 1.4077 1.1839 1.8879 1.2585 1.7456 1.5364 1.4618 1.4489 1.5118
1891.3964 1.6226 1.4373 1.407 1.1832 1.8916 1.2572 1.7439 1.5366 1.4652 1.4479 1.5107
1901.3967 1.6228 1.4369 1.4065 1.1822 1.8953 1.2562 1.7421 1.5367 1.4683 1.4468 1.5098
1911.397 1.6231 1.4366 1.4058 1.1811 1.8995 1.2552 1.7403 1.5368 1.4715 1.4458 1.5088
1921.3974 1.6236 1.4364 1.4053 1.1802 1.9039 1.2542 1.7386 1.5368 1.4748 1.4447 1.5079
1931.398 1.6238 1.4362 1.4046 1.1792 1.9079 1.2534 1.737 1.5367 1.4785 1.4437 1.5068
1941.3985 1.6238 1.436 1.404 1.1781 1.9122 1.2527 1.7355 1.5366 1.4825 1.4426 1.5057
1951.3991 1.6238 1.4358 1.4034 1.177 1.9164 1.2522 1.7342 1.5365 1.4864 1.4416 1.5047
1961.3999 1.6238 1.4356 1.4027 1.1756 1.92 1.2515 1.7328 1.5362 1.4903 1.4404 1.5038
1971.4007 1.6239 1.4356 1.402 1.1738 1.9238 1.2509 1.7313 1.536 1.4943 1.4392 1.503
1981.4014 1.6239 1.4355 1.4013 1.1723 1.9275 1.2503 1.7299 1.5358 1.4979 1.438 1.5019
1991.4021 1.6237 1.4354 1.4005 1.1708 1.9317 1.25 1.7283 1.5355 1.5018 1.4368 1.5008
2001.4027 1.6236 1.4354 1.3997 1.1694 1.9361 1.2496 1.7267 1.5353 1.5054 1.4355 1.4996
2011.4034 1.6235 1.4354 1.399 1.1681 1.9406 1.2492 1.725 1.535 1.5087 1.4343 1.4984
2021.404 1.6236 1.4355 1.3984 1.1669 1.9455 1.249 1.7233 1.5346 1.5116 1.4332 1.497
2031.4046 1.6237 1.4356 1.3977 1.1659 1.9499 1.2485 1.7214 1.5343 1.5144 1.432 1.4954
2041.4053 1.6238 1.4357 1.3971 1.1649 1.954 1.2482 1.7197 1.5339 1.5172 1.4308 1.4938
2051.406 1.624 1.4359 1.3965 1.1639 1.9584 1.248 1.718 1.5334 1.5196 1.4295 1.4926
2061.4067 1.6243 1.436 1.3958 1.1626 1.9634 1.2477 1.7163 1.5328 1.5213 1.4282 1.4917
2071.4075 1.6246 1.4361 1.3951 1.1613 1.9689 1.2474 1.7145 1.5323 1.5226 1.427 1.4906
2081.4082 1.6249 1.4362 1.3943 1.1604 1.974 1.2469 1.7128 1.5319 1.5239 1.4257 1.4893
2091.4088 1.6251 1.4362 1.3934 1.1593 1.9787 1.2465 1.7112 1.5316 1.5252 1.4243 1.4878
2101.4095 1.6253 1.4362 1.3925 1.1581 1.9839 1.2462 1.7096 1.5313 1.5263 1.4232 1.4863
2111.4102 1.6254 1.4362 1.3916 1.1571 1.9893 1.2461 1.708 1.531 1.5272 1.4221 1.4848
2121.4111 1.6256 1.4364 1.3907 1.1564 1.9941 1.2461 1.7063 1.5305 1.5282 1.4211 1.4832
2131.4121 1.6257 1.4365 1.3897 1.1558 1.9982 1.2461 1.7047 1.5301 1.5289 1.42 1.4816
2141.413 1.6258 1.4366 1.3887 1.1553 2.0024 1.246 1.703 1.5296 1.5298 1.419 1.4798
2151.4139 1.6259 1.4367 1.3879 1.1547 2.0069 1.2459 1.7013 1.529 1.5308 1.418 1.478
2161.4148 1.6261 1.4368 1.387 1.154 2.0118 1.2457 1.6997 1.5285 1.5316 1.4169 1.4764
2171.4158 1.6264 1.4371 1.3861 1.1534 2.016 1.2455 1.6981 1.5281 1.5328 1.4161 1.4747
2181.4167 1.6267 1.4373 1.3851 1.1527 2.0193 1.2454 1.6965 1.5278 1.5344 1.4154 1.4732
2191.4176 1.627 1.4375 1.3841 1.152 2.0227 1.2455 1.6949 1.5275 1.5359 1.4145 1.4716
2201.4183 1.6271 1.4377 1.3832 1.1511 2.0252 1.2457 1.6932 1.5273 1.5372 1.4137 1.47
2211.4191 1.6273 1.4378 1.3822 1.1502 2.0277 1.2461 1.6916 1.527 1.5382 1.4129 1.4684
2221.4199 1.6275 1.4379 1.3812 1.1495 2.0311 1.2465 1.6901 1.5266 1.5391 1.4122 1.4668
2231.4207 1.6277 1.4379 1.3803 1.149 2.0345 1.2468 1.6885 1.5263 1.5401 1.4114 1.4653
2241.4216 1.628 1.438 1.3793 1.1487 2.0385 1.2471 1.687 1.5261 1.5414 1.4106 1.4637
2251.4223 1.6283 1.4379 1.3784 1.1482 2.042 1.2473 1.6855 1.5258 1.5426 1.4097 1.462
2261.4232 1.6287 1.4377 1.3775 1.1478 2.0457 1.2476 1.684 1.5255 1.5441 1.409 1.4602
2271.4243 1.6291 1.4376 1.3766 1.1474 2.0502 1.248 1.6825 1.5253 1.5455 1.4082 1.4583
2281.4255 1.6295 1.4375 1.3757 1.1471 2.0544 1.2484 1.681 1.5251 1.5472 1.4075 1.4566
2291.4265 1.6298 1.4374 1.3748 1.1467 2.0587 1.2491 1.6796 1.5249 1.5487 1.4068 1.4549
2301.4276 1.6304 1.4372 1.3738 1.1464 2.0642 1.2498 1.6782 1.5248 1.5498 1.406 1.4533
2311.4285 1.6312 1.437 1.3729 1.146 2.0703 1.2505 1.6768 1.5246 1.551 1.4053 1.4516
2321.4296 1.632 1.4369 1.3721 1.1458 2.076 1.2512 1.6755 1.5244 1.5517 1.4045 1.4499
2331.4306 1.6327 1.4368 1.3712 1.1459 2.0818 1.2518 1.6741 1.5242 1.552 1.4036 1.4482
2341.4315 1.6335 1.4367 1.3703 1.1459 2.0884 1.2524 1.6728 1.5241 1.552 1.4027 1.4465
2351.4326 1.6344 1.4363 1.3694 1.1456 2.0958 1.2529 1.6715 1.524 1.552 1.4019 1.4448
2361.4337 1.6352 1.4358 1.3684 1.1453 2.1033 1.2534 1.6702 1.5239 1.5522 1.4012 1.443
2371.4348 1.636 1.4355 1.3676 1.1453 2.1116 1.2541 1.6688 1.5237 1.5524 1.4004 1.4412
2381.4358 1.6368 1.4352 1.3668 1.1453 2.1198 1.2548 1.6675 1.5236 1.5521 1.3994 1.4394
2391.4367 1.6376 1.4349 1.366 1.1451 2.1273 1.2557 1.6661 1.5235 1.5519 1.3984 1.4377
2401.4377 1.6385 1.4346 1.3654 1.1447 2.135 1.2565 1.6647 1.5235 1.5518 1.3974 1.436
2411.4387 1.6395 1.4342 1.3648 1.1444 2.1426 1.2574 1.6632 1.5236 1.5513 1.3964 1.4344
2421.4398 1.6405 1.4338 1.3642 1.1441 2.1492 1.2583 1.6618 1.5236 1.5506 1.3955 1.4327
2431.4409 1.6414 1.4333 1.3636 1.1438 2.1555 1.259 1.6604 1.5236 1.5498 1.3945 1.4309
2441.4419 1.6423 1.4329 1.3631 1.1435 2.1617 1.2597 1.659 1.5237 1.549 1.3934 1.4293
2451.4428 1.6434 1.4323 1.3625 1.1432 2.1676 1.2604 1.6576 1.5237 1.5481 1.3924 1.4277
2461.4436 1.6444 1.4318 1.3619 1.143 2.1742 1.261 1.6561 1.5238 1.5474 1.3914 1.426
2471.4446 1.6453 1.4312 1.3613 1.1429 2.1811 1.2616 1.6547 1.5239 1.5467 1.3903 1.4244
2481.4456 1.6463 1.4305 1.3607 1.1427 2.1878 1.2623 1.6532 1.524 1.546 1.3893 1.4229
2491.4468 1.6473 1.4297 1.3602 1.1425 2.1945 1.263 1.6518 1.5244 1.5451 1.3882 1.4215
2501.448 1.6483 1.4289 1.3596 1.142 2.2013 1.2638 1.6503 1.5248 1.5443 1.3872 1.4201

Data for figure immediately follows

Data for Appendix 4 - Long Memory Hypothesis Tests: USD Bilateral Exchange Rate (Singapore - Norway)

xiSingaporeThailandIsraelNigeriaSouth AfricaTurkeyAustraliaCanadaCzech RepublicEuro AreaJapanNorway
01.259 1.6007 1.9974 0.6878 2.0043 1.2331 1.3057 1.6517 1.709 1.5111 1.2624 1.4285
11.3047 1.5518 2.0328 0.8408 2.0133 1.3126 1.2875 1.6396 1.7005 1.5084 1.245 1.4301
21.3233 1.5585 2.0516 0.9287 2.0264 1.3468 1.2901 1.6423 1.7064 1.5005 1.2335 1.4371
31.3349 1.574 2.082 1.0072 2.0394 1.3546 1.3029 1.6476 1.7054 1.501 1.228 1.4446
41.3394 1.5785 2.0998 1.0555 2.0452 1.3561 1.3117 1.6543 1.6877 1.4924 1.2246 1.4435
51.3341 1.5639 2.1042 1.0922 2.046 1.3551 1.318 1.6613 1.6814 1.4889 1.2205 1.4418
61.3417 1.5565 2.1112 1.1134 2.0425 1.3676 1.3246 1.6669 1.6769 1.4868 1.2187 1.4437
71.3476 1.5548 2.1125 1.1336 2.0401 1.3727 1.3298 1.6644 1.6662 1.4826 1.2164 1.4441
81.3542 1.5582 2.1002 1.1553 2.0312 1.3756 1.3345 1.6606 1.6602 1.4791 1.213 1.4421
91.3566 1.5618 2.0856 1.2015 2.0131 1.3751 1.3378 1.6582 1.6553 1.4782 1.2088 1.4393
101.3516 1.5601 2.0711 1.211 2.0005 1.3699 1.3408 1.6564 1.649 1.4775 1.2005 1.4352
111.3509 1.5578 2.0581 1.2242 1.9905 1.3683 1.3439 1.6553 1.6437 1.477 1.1931 1.4312
121.347 1.5501 2.0451 1.2444 1.9855 1.3662 1.3443 1.653 1.64 1.478 1.1866 1.4291
131.3437 1.5421 2.0297 1.2703 1.9846 1.3609 1.3467 1.6489 1.635 1.476 1.1813 1.4279
141.3412 1.5352 2.0164 1.2853 1.9794 1.3541 1.3494 1.6455 1.6291 1.4729 1.1757 1.424
151.339 1.5314 2.0007 1.3007 1.9691 1.3423 1.3528 1.6457 1.6295 1.4715 1.1705 1.4195
161.3379 1.5279 1.9873 1.3102 1.9609 1.3295 1.3567 1.6468 1.6306 1.4709 1.1659 1.4165
171.3339 1.5192 1.9767 1.3059 1.9551 1.3167 1.3596 1.6482 1.6308 1.4684 1.1627 1.4139
181.3297 1.5116 1.9688 1.3174 1.9491 1.3084 1.3613 1.6486 1.6325 1.4682 1.1589 1.4132
191.3243 1.5026 1.9601 1.331 1.9436 1.3006 1.3622 1.6485 1.634 1.4656 1.1561 1.4132
201.3199 1.4939 1.9534 1.3262 1.9396 1.2949 1.3623 1.6463 1.635 1.462 1.1531 1.4122
211.3156 1.4879 1.9452 1.3329 1.9361 1.2887 1.3616 1.6454 1.6367 1.4578 1.1506 1.4105
221.312 1.4824 1.9377 1.3379 1.9319 1.2846 1.3604 1.6445 1.6379 1.4548 1.1484 1.4095
231.3092 1.4791 1.9305 1.3492 1.9267 1.2844 1.3599 1.643 1.6368 1.451 1.1463 1.4076
241.3081 1.4755 1.9249 1.3548 1.9209 1.2809 1.3599 1.6428 1.6354 1.4461 1.1447 1.406
251.3057 1.4733 1.92 1.3612 1.915 1.2791 1.3596 1.6431 1.6336 1.4398 1.1428 1.4041
261.3044 1.4733 1.9144 1.3709 1.9094 1.2757 1.3591 1.6432 1.6298 1.4334 1.1409 1.4025
271.3025 1.4727 1.9103 1.3778 1.9023 1.2719 1.3587 1.6427 1.6261 1.428 1.139 1.4012
281.3008 1.4693 1.906 1.3856 1.8963 1.2695 1.3588 1.6416 1.6236 1.4236 1.1371 1.3993
291.2991 1.4628 1.9031 1.399 1.8921 1.2648 1.3589 1.6407 1.6224 1.4211 1.1355 1.3983
301.298 1.4565 1.9 1.4033 1.8876 1.2593 1.3591 1.639 1.6214 1.4175 1.1344 1.3982
311.2978 1.4508 1.8975 1.4053 1.8849 1.2568 1.3593 1.6382 1.6201 1.4145 1.1335 1.398
321.2982 1.4447 1.8948 1.4175 1.8825 1.2563 1.3602 1.6378 1.6175 1.4108 1.1325 1.3977
331.298 1.4381 1.8922 1.4219 1.8802 1.2574 1.3611 1.6375 1.615 1.4082 1.1316 1.3984
341.2976 1.4305 1.8923 1.428 1.8778 1.2585 1.3614 1.6363 1.6122 1.4053 1.1309 1.3992
351.2972 1.4243 1.8898 1.4379 1.8749 1.2617 1.3616 1.635 1.6102 1.4024 1.1297 1.399
361.2966 1.4219 1.8875 1.4404 1.8712 1.2628 1.3616 1.6344 1.6083 1.4 1.1286 1.399
371.2966 1.4211 1.8855 1.4359 1.869 1.265 1.3624 1.6339 1.6069 1.3981 1.128 1.399
381.2964 1.419 1.8831 1.4428 1.8669 1.2678 1.3634 1.6333 1.6062 1.3971 1.1274 1.3984
391.2965 1.4159 1.881 1.4464 1.8645 1.2696 1.3646 1.6329 1.6053 1.3972 1.1269 1.3975
401.2954 1.4138 1.878 1.4435 1.8615 1.2704 1.3652 1.6319 1.6037 1.3961 1.126 1.3963
411.2952 1.4125 1.875 1.4462 1.8593 1.2709 1.3662 1.6314 1.6032 1.3956 1.1253 1.3955
421.2946 1.4112 1.8719 1.4526 1.8574 1.2721 1.3673 1.6316 1.6034 1.3955 1.1245 1.3947
431.2942 1.4106 1.8679 1.4596 1.8551 1.2737 1.3681 1.6326 1.603 1.3954 1.1236 1.3938
441.2939 1.4103 1.8637 1.4622 1.8526 1.274 1.3688 1.6326 1.6016 1.3949 1.1226 1.3926
451.2933 1.4103 1.8606 1.4706 1.8506 1.2734 1.3697 1.6324 1.6009 1.3952 1.1216 1.3915
461.2935 1.4101 1.8579 1.4799 1.8492 1.273 1.3709 1.6327 1.6008 1.3956 1.1208 1.3903
471.2944 1.4083 1.8557 1.4904 1.848 1.2722 1.3727 1.6328 1.6008 1.3952 1.12 1.3894
481.2958 1.4069 1.854 1.4995 1.8475 1.2723 1.3741 1.6334 1.6001 1.3945 1.1196 1.3885
491.2972 1.4056 1.8523 1.5091 1.8468 1.2719 1.3755 1.6342 1.5991 1.394 1.1194 1.3877
501.2984 1.4061 1.851 1.5162 1.8459 1.2722 1.377 1.6352 1.598 1.3937 1.1194 1.3871
511.2994 1.4061 1.8496 1.527 1.8446 1.271 1.3784 1.6357 1.5969 1.393 1.1195 1.3864
521.2997 1.406 1.8484 1.5356 1.8432 1.2703 1.3801 1.6367 1.5963 1.3929 1.1195 1.3857
531.2998 1.4072 1.8483 1.5402 1.8419 1.2698 1.3819 1.6381 1.5961 1.3927 1.1196 1.3851
541.2997 1.4088 1.8473 1.5469 1.8404 1.269 1.3837 1.6395 1.5952 1.392 1.1193 1.3841
551.3001 1.4106 1.8469 1.5524 1.8386 1.2677 1.3854 1.6408 1.5941 1.3915 1.119 1.3833
561.3011 1.4129 1.8461 1.5561 1.8372 1.2666 1.3875 1.642 1.5924 1.3903 1.1187 1.3824
571.3015 1.4163 1.845 1.5604 1.8359 1.2653 1.3888 1.6429 1.5908 1.3886 1.1181 1.3814
581.302 1.4185 1.8449 1.5654 1.8349 1.2638 1.3901 1.6437 1.5891 1.3872 1.1176 1.3807
591.3028 1.4205 1.8452 1.5711 1.8337 1.2629 1.3912 1.6443 1.5877 1.3859 1.1171 1.3798
601.3032 1.4221 1.8454 1.578 1.8325 1.2619 1.3921 1.645 1.5865 1.3845 1.1162 1.3791
611.3033 1.423 1.8457 1.5859 1.8313 1.2606 1.3931 1.6459 1.5858 1.3842 1.1154 1.3787
621.3033 1.4237 1.8463 1.5932 1.8302 1.2603 1.3944 1.6465 1.5854 1.3837 1.1146 1.3782
631.3039 1.424 1.8465 1.5964 1.8293 1.2605 1.3953 1.647 1.5844 1.3834 1.1138 1.3775
641.3046 1.4237 1.8472 1.6038 1.8278 1.2591 1.3958 1.647 1.5829 1.383 1.1127 1.3769
651.3053 1.424 1.8478 1.6107 1.8259 1.2578 1.3964 1.6475 1.5815 1.3833 1.1118 1.3766
661.3069 1.4243 1.8484 1.6179 1.8242 1.2572 1.3966 1.6482 1.5804 1.384 1.1109 1.3759
671.3083 1.4239 1.8486 1.6224 1.8226 1.256 1.397 1.6486 1.5795 1.3841 1.1101 1.3755
681.3094 1.4235 1.8493 1.6277 1.8209 1.2542 1.3974 1.649 1.5783 1.384 1.1091 1.3752
691.3105 1.4234 1.8499 1.6327 1.8189 1.2532 1.3977 1.6489 1.5772 1.3844 1.1083 1.3752
701.3116 1.4239 1.8502 1.6396 1.8166 1.2506 1.3979 1.6491 1.5756 1.3847 1.1074 1.3751
711.3126 1.4237 1.8498 1.6479 1.8145 1.2487 1.398 1.6493 1.5742 1.3854 1.1065 1.3748
721.3134 1.4233 1.8498 1.6583 1.8124 1.2468 1.3982 1.6499 1.5733 1.3865 1.1058 1.3744
731.3141 1.4225 1.8499 1.6617 1.8109 1.2445 1.399 1.6505 1.5722 1.3877 1.1052 1.3741
741.315 1.423 1.8503 1.6728 1.8095 1.242 1.3997 1.6514 1.571 1.3889 1.1045 1.3737
751.3162 1.4241 1.8504 1.6814 1.8084 1.2392 1.4006 1.6524 1.5696 1.3902 1.104 1.3733
761.3179 1.4257 1.8501 1.69 1.8072 1.237 1.4016 1.6533 1.5689 1.3918 1.1036 1.373
771.3192 1.4273 1.8498 1.6983 1.8064 1.2354 1.4024 1.6543 1.5682 1.393 1.103 1.3725
781.3202 1.4288 1.8498 1.7054 1.8057 1.2346 1.4029 1.655 1.5675 1.3946 1.1027 1.3722
791.3214 1.4307 1.8501 1.7163 1.8049 1.2337 1.4034 1.6558 1.5674 1.3956 1.1023 1.3723
801.3226 1.4323 1.8502 1.7228 1.8042 1.2332 1.4037 1.656 1.5669 1.3963 1.1018 1.3724
811.3238 1.434 1.8503 1.7325 1.8035 1.2321 1.4044 1.6556 1.5664 1.3967 1.1014 1.3724
821.3251 1.436 1.8505 1.7457 1.8028 1.2313 1.4048 1.6553 1.566 1.3972 1.101 1.3726
831.3265 1.4378 1.8505 1.7486 1.8023 1.2306 1.4052 1.655 1.5656 1.3981 1.1006 1.3728
841.3282 1.44 1.8501 1.757 1.8015 1.2301 1.4054 1.6547 1.5656 1.3984 1.1 1.3725
851.3295 1.4429 1.8496 1.7687 1.8004 1.2294 1.4057 1.6543 1.5659 1.399 1.0994 1.3723
861.3308 1.4458 1.8492 1.7795 1.7995 1.229 1.406 1.654 1.5663 1.3999 1.0988 1.3722
871.3321 1.4485 1.8484 1.7914 1.7983 1.2286 1.4062 1.6533 1.5666 1.4004 1.0982 1.3721
881.3337 1.4515 1.8473 1.8034 1.7971 1.2279 1.4065 1.6527 1.567 1.4011 1.0978 1.3724
891.3353 1.4547 1.8463 1.8081 1.7961 1.2271 1.407 1.652 1.5672 1.4012 1.0974 1.3726
901.3365 1.4578 1.8456 1.8155 1.795 1.2262 1.4074 1.6513 1.5672 1.4011 1.0969 1.3727
911.338 1.4604 1.8451 1.8236 1.794 1.225 1.4077 1.6505 1.5671 1.4008 1.0965 1.3727
921.3395 1.4626 1.8441 1.8331 1.7931 1.2242 1.4084 1.6495 1.567 1.401 1.0962 1.3731
931.3413 1.4638 1.8437 1.8399 1.7923 1.2237 1.4091 1.649 1.5673 1.4019 1.0959 1.3737
941.3428 1.4648 1.8431 1.8461 1.7912 1.2227 1.4094 1.6486 1.5672 1.4023 1.0955 1.3741
951.3441 1.4658 1.842 1.8506 1.7902 1.222 1.4102 1.648 1.567 1.4031 1.0953 1.3746
961.3455 1.4665 1.8406 1.8554 1.7893 1.2215 1.4111 1.6477 1.5671 1.4042 1.095 1.3752
971.3469 1.4667 1.8389 1.8528 1.7887 1.2207 1.412 1.6471 1.5669 1.4049 1.0947 1.3757
981.3483 1.4671 1.8367 1.8609 1.7884 1.2201 1.4129 1.6467 1.5665 1.4056 1.0943 1.3761
991.35 1.4682 1.8346 1.8625 1.7881 1.2194 1.4138 1.6459 1.5658 1.4061 1.0938 1.3763
1001.3514 1.4691 1.8326 1.864 1.7881 1.2183 1.4145 1.6449 1.5651 1.4065 1.0935 1.3764
1011.3533 1.4698 1.8314 1.8665 1.7882 1.2177 1.4153 1.6441 1.5646 1.4072 1.0932 1.3767
1021.355 1.4705 1.8299 1.8715 1.7885 1.2172 1.416 1.6434 1.564 1.4078 1.0929 1.3772
1031.3569 1.4713 1.8282 1.8753 1.7888 1.2165 1.4165 1.6426 1.5628 1.4081 1.0926 1.3774
1041.359 1.473 1.8262 1.8772 1.7887 1.2163 1.4169 1.6418 1.5615 1.4083 1.0923 1.3774
1051.361 1.4742 1.8241 1.8757 1.7888 1.2165 1.4174 1.641 1.5603 1.4088 1.092 1.3775
1061.3627 1.4755 1.8221 1.8803 1.7892 1.2167 1.418 1.6401 1.559 1.4091 1.0917 1.3775
1071.3642 1.4769 1.8202 1.8817 1.7897 1.2172 1.4187 1.6387 1.5579 1.4096 1.0915 1.3775
1081.3658 1.479 1.8183 1.8854 1.7901 1.218 1.4191 1.6374 1.5566 1.41 1.0914 1.3775
1091.3674 1.481 1.8162 1.8902 1.7908 1.2183 1.4195 1.6361 1.5554 1.4105 1.0914 1.3776
1101.3686 1.4821 1.8139 1.8967 1.7917 1.2185 1.4199 1.6348 1.5542 1.4104 1.0913 1.3775
1111.3697 1.4825 1.8115 1.8954 1.7924 1.2184 1.4203 1.6336 1.5533 1.4103 1.0912 1.3774
1121.3706 1.4829 1.8092 1.8973 1.793 1.2188 1.4205 1.6321 1.5522 1.4101 1.091 1.3772
1131.3718 1.4834 1.8068 1.8982 1.7932 1.2194 1.4208 1.6305 1.5512 1.4097 1.0909 1.3769
1141.3731 1.4842 1.8046 1.9006 1.7937 1.22 1.4212 1.6289 1.55 1.4093 1.091 1.3767
1151.3745 1.485 1.8028 1.9056 1.7943 1.2201 1.4216 1.6272 1.5489 1.4089 1.091 1.3766
1161.3764 1.4865 1.8013 1.9084 1.7951 1.2209 1.4222 1.6254 1.5477 1.4086 1.0912 1.3765
1171.3781 1.488 1.7998 1.9112 1.7962 1.2216 1.4226 1.6239 1.547 1.4089 1.0913 1.3767
1181.3805 1.4892 1.7983 1.9152 1.7971 1.2221 1.423 1.6225 1.5462 1.409 1.0916 1.377
1191.3826 1.4904 1.7965 1.9199 1.7976 1.2223 1.4236 1.6212 1.5454 1.4091 1.0919 1.3773
1201.3848 1.4916 1.7946 1.9222 1.798 1.2229 1.4243 1.6197 1.5446 1.4093 1.092 1.3777
1211.3868 1.4923 1.7929 1.9241 1.7985 1.2231 1.4249 1.6185 1.5436 1.4097 1.0921 1.3782
1221.3886 1.4924 1.7914 1.9279 1.7992 1.2239 1.4257 1.6176 1.5425 1.4102 1.0924 1.3786
1231.3907 1.4925 1.7896 1.9363 1.8 1.2249 1.4261 1.6167 1.5415 1.4107 1.0927 1.3791
1241.3922 1.4924 1.7879 1.9408 1.8012 1.2257 1.4265 1.6158 1.5406 1.4108 1.0929 1.3797
1251.3938 1.4923 1.786 1.9453 1.8027 1.2265 1.4269 1.6151 1.5399 1.4111 1.0931 1.3804
1261.3954 1.4927 1.7843 1.9498 1.8039 1.2274 1.4273 1.6144 1.5391 1.4114 1.0933 1.3808
1271.3965 1.4929 1.7827 1.9521 1.8049 1.2279 1.4276 1.6135 1.5381 1.4116 1.0936 1.3813
1281.3978 1.4936 1.7813 1.9554 1.806 1.2281 1.4279 1.6127 1.5372 1.4122 1.094 1.3818
1291.3987 1.4936 1.7798 1.9601 1.8072 1.2285 1.4282 1.6119 1.5361 1.4125 1.0943 1.3823
1301.3996 1.4937 1.7781 1.9616 1.8086 1.2289 1.4284 1.6111 1.5351 1.4132 1.0945 1.3828
1311.4005 1.4936 1.7764 1.966 1.8102 1.2292 1.4286 1.6104 1.534 1.4136 1.0947 1.3833
1321.4013 1.494 1.7747 1.967 1.812 1.2293 1.4289 1.6097 1.5332 1.4142 1.095 1.3839
1331.4028 1.495 1.773 1.9705 1.8136 1.2294 1.4291 1.6091 1.5324 1.4151 1.0953 1.3846
1341.4041 1.4958 1.7716 1.9737 1.815 1.2293 1.429 1.6086 1.5317 1.4159 1.0958 1.3853
1351.4055 1.4965 1.7704 1.9778 1.8164 1.2293 1.4289 1.6079 1.531 1.4165 1.0962 1.3859
1361.4068 1.4973 1.7691 1.9782 1.8178 1.2292 1.4288 1.6072 1.5306 1.417 1.0967 1.3865
1371.4083 1.4991 1.7677 1.9826 1.8192 1.2293 1.4285 1.6065 1.5301 1.4173 1.0973 1.3871
1381.4099 1.501 1.7663 1.9864 1.8206 1.2294 1.4284 1.6058 1.5292 1.4172 1.098 1.3877
1391.4109 1.5023 1.765 1.988 1.8218 1.2292 1.4284 1.6051 1.5283 1.417 1.0987 1.3883
1401.4123 1.5035 1.7638 1.9884 1.823 1.229 1.4285 1.6044 1.5273 1.4169 1.0993 1.3888
1411.4137 1.5043 1.7626 1.99 1.8243 1.2286 1.4286 1.6039 1.5265 1.4168 1.1 1.3893
1421.415 1.5051 1.7613 1.9945 1.8257 1.2286 1.4286 1.6035 1.5256 1.4165 1.1007 1.3896
1431.4163 1.5062 1.76 1.9987 1.8272 1.2282 1.4284 1.6031 1.5247 1.4166 1.1014 1.3899
1441.4174 1.5072 1.7586 1.9998 1.8288 1.2279 1.4282 1.6026 1.5238 1.4165 1.1021 1.3901
1451.4184 1.5088 1.757 2.0023 1.8303 1.2277 1.428 1.6022 1.5229 1.4163 1.1029 1.3903
1461.4193 1.5108 1.7553 2.0057 1.8319 1.2274 1.4276 1.6018 1.5221 1.4162 1.1038 1.3906
1471.4204 1.513 1.7538 2.0113 1.8336 1.2271 1.4273 1.6014 1.5217 1.4161 1.1045 1.3909
1481.4211 1.5152 1.7524 2.0157 1.835 1.2268 1.4269 1.6011 1.5211 1.4156 1.1051 1.3912
1491.4217 1.5178 1.751 2.0152 1.8365 1.2264 1.4268 1.6007 1.5207 1.4152 1.1057 1.3913
1501.4226 1.5203 1.7498 2.0167 1.8383 1.2262 1.4265 1.6001 1.5203 1.4146 1.1063 1.3915
1511.4235 1.5225 1.7488 2.0166 1.84 1.226 1.4263 1.5996 1.5202 1.4141 1.107 1.3918
1521.4243 1.5246 1.7478 2.0191 1.8419 1.2259 1.4263 1.5993 1.5198 1.4139 1.1077 1.3922
1531.4251 1.5267 1.7467 2.0221 1.8436 1.2261 1.4261 1.5991 1.5193 1.4136 1.1084 1.3926
1541.426 1.5288 1.7455 2.0234 1.845 1.2263 1.4258 1.5991 1.5188 1.4133 1.109 1.393
1551.427 1.5309 1.7443 2.0272 1.8462 1.2261 1.4255 1.5991 1.5185 1.4131 1.1097 1.3934
1561.4278 1.5328 1.7432 2.0235 1.8471 1.226 1.4252 1.5992 1.5183 1.4129 1.1104 1.3937
1571.4287 1.5345 1.7423 2.0196 1.848 1.2259 1.4248 1.5993 1.518 1.4128 1.111 1.394
1581.4297 1.5356 1.7417 2.021 1.8489 1.2255 1.4247 1.5996 1.5174 1.4124 1.1116 1.3942
1591.4303 1.5366 1.7413 2.0258 1.8497 1.2252 1.4246 1.5997 1.5167 1.4117 1.1122 1.3944
1601.431 1.5377 1.7408 2.0272 1.8505 1.225 1.4243 1.5997 1.516 1.4112 1.1127 1.3944
1611.432 1.5388 1.7403 2.0318 1.8513 1.2249 1.4241 1.5997 1.5153 1.4107 1.1131 1.3945
1621.4329 1.5395 1.7398 2.0356 1.8518 1.2248 1.4237 1.5997 1.5147 1.4101 1.1135 1.3946
1631.4336 1.5398 1.7393 2.0401 1.8522 1.2248 1.4233 1.5996 1.5139 1.4094 1.1139 1.3946
1641.434 1.54 1.7387 2.0404 1.8525 1.2248 1.423 1.5994 1.513 1.4084 1.1143 1.3946
1651.4345 1.54 1.738 2.0429 1.8527 1.2251 1.4225 1.5994 1.5121 1.4075 1.1147 1.3947
1661.4351 1.5404 1.7375 2.048 1.853 1.2252 1.4219 1.5995 1.5111 1.4063 1.1151 1.3948
1671.4354 1.5408 1.7371 2.0472 1.8535 1.2253 1.4214 1.5995 1.5101 1.405 1.1155 1.3949
1681.4359 1.5412 1.7366 2.0494 1.854 1.2255 1.421 1.5993 1.5093 1.4038 1.1159 1.3948
1691.436 1.5411 1.7361 2.0513 1.8541 1.2259 1.4205 1.599 1.5086 1.4025 1.1164 1.3947
1701.4364 1.5411 1.7356 2.0554 1.8543 1.2261 1.4201 1.5987 1.5077 1.4014 1.1169 1.3945
1711.4368 1.5412 1.7351 2.0587 1.8545 1.2263 1.4195 1.5983 1.5068 1.3999 1.1174 1.3944
1721.4373 1.5418 1.7345 2.0606 1.8544 1.2265 1.4187 1.5981 1.5059 1.3983 1.1178 1.3942
1731.4378 1.5421 1.734 2.0645 1.8542 1.2266 1.4182 1.5978 1.505 1.3968 1.1182 1.3939
1741.4382 1.5425 1.7334 2.0659 1.8537 1.2266 1.4178 1.5974 1.5043 1.3953 1.1186 1.3937
1751.4385 1.5429 1.7327 2.0703 1.853 1.2265 1.4172 1.597 1.5036 1.394 1.1188 1.3935
1761.4387 1.5432 1.7321 2.0727 1.8523 1.2267 1.4168 1.5967 1.5028 1.3928 1.119 1.3933
1771.4389 1.544 1.7314 2.0748 1.8515 1.2271 1.4161 1.5963 1.502 1.3916 1.1192 1.393
1781.4391 1.5445 1.7309 2.0779 1.8507 1.2274 1.4154 1.596 1.5012 1.3902 1.1194 1.3926
1791.439 1.545 1.73 2.0801 1.8498 1.2275 1.4148 1.5956 1.5005 1.3889 1.1196 1.3924
1801.4388 1.5452 1.7291 2.0803 1.849 1.2279 1.4143 1.5951 1.4998 1.3874 1.1197 1.3922
1811.4382 1.5454 1.7282 2.0851 1.8482 1.2283 1.4138 1.5945 1.499 1.386 1.1197 1.392
1821.4377 1.5454 1.7273 2.0872 1.8476 1.2286 1.4134 1.5939 1.4983 1.3846 1.1198 1.3918
1831.4372 1.5454 1.7264 2.0912 1.8469 1.2288 1.4129 1.5935 1.4974 1.3831 1.1198 1.3917
1841.4368 1.5453 1.7255 2.0912 1.8461 1.229 1.4125 1.593 1.4966 1.3815 1.1198 1.3916
1851.4365 1.5451 1.7245 2.0948 1.8453 1.229 1.4119 1.5926 1.4957 1.3798 1.1198 1.3914
1861.4363 1.5452 1.7235 2.0967 1.8445 1.229 1.4113 1.5922 1.495 1.3784 1.1198 1.3914
1871.4361 1.5452 1.7223 2.0953 1.8438 1.2292 1.4105 1.5917 1.4943 1.377 1.1198 1.3914
1881.436 1.5451 1.7211 2.096 1.8429 1.2291 1.4096 1.5912 1.4936 1.3754 1.1196 1.3914
1891.4359 1.5449 1.7198 2.0975 1.842 1.2291 1.4087 1.5906 1.4927 1.3738 1.1195 1.3914
1901.4358 1.5448 1.7184 2.0974 1.8412 1.2292 1.4079 1.5903 1.4919 1.3724 1.1192 1.3914
1911.4354 1.5446 1.7171 2.0979 1.8402 1.2292 1.4071 1.5899 1.491 1.3707 1.1189 1.3915
1921.435 1.5442 1.7158 2.0987 1.8392 1.2293 1.4063 1.5896 1.4901 1.3691 1.1187 1.3915
1931.4345 1.544 1.7146 2.0971 1.8383 1.2296 1.4054 1.5891 1.4891 1.3672 1.1184 1.3915
1941.4342 1.544 1.7132 2.0966 1.8374 1.2296 1.4046 1.5884 1.4883 1.3655 1.1182 1.3915
1951.4338 1.544 1.7119 2.098 1.8365 1.2298 1.4037 1.5879 1.4875 1.3637 1.1179 1.3915
1961.4334 1.544 1.7105 2.0959 1.8355 1.2298 1.4029 1.5873 1.4866 1.3617 1.1177 1.3914
1971.433 1.5441 1.709 2.0922 1.8345 1.2298 1.4021 1.5867 1.486 1.3599 1.1175 1.3915
1981.4327 1.5443 1.7075 2.0935 1.8333 1.2297 1.4015 1.5861 1.4855 1.3582 1.1172 1.3916
1991.4324 1.5447 1.7061 2.0933 1.8322 1.2298 1.4009 1.5855 1.485 1.3568 1.1169 1.3918
2001.4321 1.5451 1.7046 2.0919 1.8308 1.2297 1.4002 1.5848 1.4846 1.3553 1.1166 1.3919
2011.4318 1.5454 1.7032 2.088 1.8295 1.2296 1.3995 1.5841 1.484 1.3537 1.1163 1.392
2021.4317 1.5455 1.7019 2.0864 1.8283 1.2296 1.3989 1.5836 1.4834 1.3523 1.1161 1.3921
2031.4313 1.5455 1.7005 2.0881 1.827 1.2295 1.3984 1.5831 1.4828 1.3508 1.1157 1.3922
2041.4309 1.5455 1.6992 2.0819 1.8258 1.2295 1.3979 1.5826 1.4823 1.3492 1.1153 1.3923
2051.4306 1.5457 1.6977 2.0832 1.8247 1.2298 1.3973 1.5823 1.4818 1.3477 1.1149 1.3923
2061.4302 1.5458 1.6963 2.0827 1.8236 1.2299 1.3967 1.582 1.4815 1.3463 1.1144 1.3923
2071.4298 1.546 1.6948 2.0788 1.8223 1.23 1.3962 1.5816 1.4812 1.3448 1.1139 1.3923
2081.4294 1.5461 1.6932 2.0784 1.821 1.2302 1.3957 1.5814 1.4809 1.3432 1.1134 1.3922
2091.4288 1.5462 1.6916 2.0777 1.8197 1.2304 1.3953 1.5813 1.4805 1.3416 1.113 1.3922
2101.4284 1.5464 1.6901 2.0762 1.8185 1.2306 1.3949 1.5812 1.4801 1.3401 1.1126 1.3921
2111.4281 1.5464 1.6888 2.0754 1.8173 1.2308 1.3945 1.5811 1.4798 1.3387 1.1123 1.392
2121.4279 1.5465 1.6874 2.073 1.816 1.2311 1.394 1.5809 1.4795 1.3374 1.112 1.392
2131.4277 1.5468 1.686 2.0705 1.8145 1.2315 1.3936 1.5807 1.479 1.336 1.1117 1.3919
2141.4273 1.5472 1.6845 2.0693 1.8132 1.232 1.3932 1.5803 1.4786 1.3347 1.1115 1.3918
2151.4269 1.5475 1.6829 2.069 1.8118 1.2325 1.3928 1.5798 1.4781 1.3333 1.1113 1.3917
2161.4264 1.5477 1.6814 2.0674 1.8104 1.233 1.3924 1.5794 1.4777 1.3319 1.1111 1.3917
2171.4258 1.5481 1.6799 2.0692 1.809 1.2336 1.3919 1.5789 1.4772 1.3305 1.1108 1.3916
2181.4254 1.5487 1.6785 2.0686 1.8076 1.234 1.3915 1.5785 1.4769 1.329 1.1105 1.3916
2191.4251 1.5494 1.6771 2.0686 1.8063 1.2343 1.3911 1.5781 1.4766 1.3277 1.1104 1.3916
2201.4247 1.5499 1.6758 2.07 1.8052 1.2347 1.3907 1.5777 1.4763 1.3263 1.1102 1.3917
2211.4243 1.5504 1.6744 2.0664 1.8039 1.2351 1.3902 1.5771 1.4759 1.3249 1.1101 1.3917
2221.424 1.5509 1.6731 2.0664 1.8025 1.2354 1.3897 1.5767 1.4756 1.3235 1.1101 1.3918
2231.4238 1.5514 1.6719 2.0674 1.8011 1.2357 1.3893 1.5762 1.4753 1.3221 1.11 1.3918
2241.4237 1.5518 1.6708 2.0668 1.7996 1.2358 1.3889 1.5757 1.4749 1.3206 1.1099 1.3918
2251.4235 1.5522 1.6695 2.0654 1.7981 1.2358 1.3886 1.5753 1.4745 1.3193 1.1097 1.3917
2261.4233 1.5525 1.6683 2.0643 1.7967 1.236 1.3882 1.5748 1.4742 1.3176 1.1095 1.3916
2271.423 1.5529 1.6672 2.0622 1.7954 1.236 1.3878 1.5742 1.4738 1.3159 1.1093 1.3914
2281.4227 1.5533 1.6659 2.0634 1.7942 1.2361 1.3874 1.5735 1.4733 1.3142 1.1091 1.391
2291.4224 1.5538 1.6645 2.0614 1.793 1.2363 1.3869 1.5727 1.4727 1.3125 1.1089 1.3907
2301.4223 1.5542 1.6632 2.0604 1.7918 1.2364 1.3865 1.5719 1.4721 1.3109 1.1086 1.3905
2311.4221 1.5545 1.662 2.0587 1.7907 1.2365 1.386 1.5711 1.4716 1.3093 1.1084 1.3903
2321.422 1.5548 1.6608 2.0556 1.7896 1.2365 1.3855 1.5701 1.4711 1.3077 1.1081 1.3901
2331.4217 1.5552 1.6597 2.0549 1.7884 1.2368 1.3849 1.5693 1.4706 1.3062 1.1077 1.3899
2341.4211 1.5555 1.6586 2.0545 1.7873 1.237 1.3844 1.5685 1.47 1.3047 1.1073 1.3897
2351.4206 1.556 1.6574 2.0537 1.7862 1.2371 1.3839 1.5677 1.4695 1.3032 1.1068 1.3895
2361.42 1.5565 1.6563 2.0547 1.7852 1.2369 1.3834 1.567 1.4689 1.3015 1.1064 1.3893
2371.4195 1.557 1.6552 2.0534 1.7842 1.2369 1.3829 1.5662 1.4683 1.2999 1.1059 1.389
2381.4189 1.5575 1.6541 2.0541 1.7832 1.2368 1.3824 1.5655 1.4677 1.2983 1.1055 1.3888
2391.4183 1.5581 1.6532 2.0558 1.7821 1.2367 1.3819 1.5647 1.467 1.2966 1.105 1.3885
2401.418 1.5587 1.6522 2.054 1.7809 1.2365 1.3813 1.5637 1.4664 1.2948 1.1044 1.3881
2411.4177 1.5595 1.6511 2.0521 1.7798 1.2366 1.3807 1.5627 1.4658 1.2931 1.1039 1.3876
2421.4174 1.5604 1.65 2.0537 1.7787 1.2367 1.3801 1.5618 1.4653 1.2915 1.1033 1.3872
2431.417 1.5613 1.6489 2.0538 1.7774 1.2367 1.3796 1.561 1.4647 1.2899 1.1027 1.3867
2441.4168 1.5621 1.6478 2.0563 1.7761 1.2369 1.3791 1.5601 1.4641 1.2884 1.1022 1.3862
2451.4166 1.5629 1.6467 2.0542 1.7746 1.237 1.3785 1.5594 1.4635 1.2868 1.1016 1.3857
2461.4164 1.5638 1.6458 2.0539 1.7732 1.2371 1.3779 1.5586 1.463 1.2853 1.1011 1.3853
2471.4161 1.5648 1.6448 2.0537 1.7717 1.2372 1.3771 1.5578 1.4623 1.2836 1.1006 1.3849
2481.4158 1.5659 1.6439 2.0556 1.7702 1.2374 1.3764 1.557 1.4616 1.2819 1.1 1.3845
2491.4155 1.567 1.6429 2.0556 1.7686 1.2376 1.3757 1.5562 1.461 1.2802 1.0994 1.3841
2501.4153 1.5679 1.6418 2.0556 1.7671 1.2378 1.375 1.5555 1.4603 1.2786 1.0987 1.3837
Data for figure immediately follows

Data for Appendix 4 - Long Memory Hypothesis Tests: USD Bilateral Exchange Rate (New Zealand - United Kingdom)

xiNew ZealandPolandSwedenSwitzerlandUnited Kingdom
01.4319 1.8523 1.4784 1.3872 1.4921
11.4419 1.812 1.4779 1.3779 1.4576
21.4708 1.79 1.4814 1.3749 1.4421
31.4851 1.7822 1.488 1.3746 1.4397
41.4966 1.7813 1.4878 1.3719 1.4368
51.5026 1.7789 1.4894 1.3686 1.427
61.5122 1.7875 1.4926 1.3667 1.4224
71.5173 1.7913 1.4945 1.3648 1.4192
81.5188 1.7953 1.4937 1.3602 1.4163
91.518 1.797 1.4915 1.3554 1.4117
101.5151 1.7953 1.4876 1.3499 1.408
111.5142 1.7964 1.4863 1.3452 1.4055
121.5102 1.7966 1.4862 1.3417 1.4047
131.5092 1.7945 1.4858 1.3393 1.4049
141.507 1.7898 1.4829 1.3363 1.4041
151.5045 1.7875 1.4792 1.3319 1.401
161.5039 1.7839 1.4761 1.3283 1.399
171.5034 1.779 1.4743 1.3252 1.3965
181.503 1.7745 1.4733 1.3231 1.3952
191.502 1.7704 1.472 1.3211 1.3939
201.5 1.7678 1.4687 1.3187 1.3917
211.4979 1.7655 1.465 1.3152 1.3889
221.4955 1.7636 1.4622 1.3124 1.3858
231.4943 1.7611 1.4586 1.3092 1.3823
241.4933 1.7575 1.4545 1.3058 1.3791
251.492 1.7513 1.4506 1.3024 1.3758
261.4916 1.7439 1.4475 1.3001 1.3732
271.4914 1.7374 1.4442 1.2983 1.3703
281.4903 1.7331 1.4403 1.2965 1.3672
291.4888 1.7313 1.4372 1.2951 1.3643
301.4869 1.7289 1.4341 1.2935 1.3614
311.4854 1.7274 1.4309 1.2924 1.359
321.4844 1.7254 1.4277 1.2915 1.3573
331.4839 1.7235 1.4253 1.2916 1.3556
341.4834 1.7219 1.4226 1.2918 1.3543
351.4823 1.7206 1.4197 1.2915 1.3525
361.4812 1.7201 1.417 1.291 1.3502
371.4808 1.7207 1.4146 1.2909 1.3484
381.4802 1.7216 1.4121 1.2906 1.3459
391.4799 1.7229 1.4103 1.2903 1.3432
401.479 1.724 1.4086 1.2899 1.3407
411.4789 1.725 1.407 1.2898 1.3387
421.4795 1.7264 1.4056 1.2894 1.337
431.4793 1.7274 1.4044 1.2891 1.3354
441.4793 1.7284 1.4026 1.2883 1.3334
451.4792 1.7303 1.4012 1.2874 1.3319
461.4793 1.733 1.3995 1.2864 1.3304
471.4792 1.7365 1.3983 1.2857 1.3294
481.4788 1.7394 1.3967 1.2854 1.3286
491.478 1.7413 1.3951 1.2853 1.3279
501.4772 1.7429 1.3937 1.2855 1.3277
511.4774 1.7447 1.3919 1.2857 1.3275
521.4786 1.7467 1.3903 1.286 1.3274
531.4794 1.7485 1.3888 1.2861 1.3273
541.4802 1.7495 1.3872 1.2858 1.3272
551.4807 1.751 1.3857 1.2853 1.3273
561.4808 1.7518 1.3842 1.2853 1.3278
571.4805 1.7528 1.3825 1.2849 1.328
581.4798 1.7532 1.3808 1.2845 1.328
591.4794 1.7531 1.3792 1.284 1.3281
601.4787 1.753 1.3778 1.2834 1.3281
611.4781 1.7534 1.3765 1.2834 1.3284
621.4774 1.7543 1.3751 1.283 1.3286
631.4764 1.7556 1.3738 1.2824 1.3288
641.4752 1.7566 1.3721 1.2819 1.3288
651.474 1.7572 1.3707 1.2816 1.3288
661.4731 1.7575 1.3692 1.2812 1.3287
671.4718 1.7582 1.3675 1.281 1.3288
681.4706 1.7585 1.3659 1.2809 1.3288
691.4695 1.7594 1.3646 1.281 1.3288
701.4682 1.7605 1.3633 1.281 1.3286
711.4669 1.7617 1.362 1.2809 1.3282
721.4653 1.7626 1.3609 1.2807 1.3279
731.4642 1.7628 1.3599 1.2804 1.3274
741.463 1.7632 1.3587 1.2801 1.3265
751.4619 1.7632 1.3574 1.2796 1.3255
761.461 1.7638 1.3563 1.2795 1.3246
771.46 1.7643 1.3553 1.2792 1.3235
781.4589 1.7642 1.3546 1.279 1.3225
791.458 1.7644 1.354 1.2789