May 1997

Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models

Matt Pritsker


A number of recent papers have used nonparametric density estimation or non- parametric regression to study the instantaneous spot interest rate, and to test term structure models. However, little is known about the performance of these methods when applied to persistent time-series, such as U.S. interest rates. This paper uses the Vasicek [1977] model to study the performance of kernel density estimates of the ergodic distribution of the instantaneous spot rate. The model's tractability allows me to analyze the MISE of the kernel estimate as a function of persistence, variance of the ergodic distribution, span of the data, sampling frequency, and kernel bandwidth. Our principle result is that persistence has an important impact on optimal bandwidth selection and on infinite sample performance. We also find that sampling the data more frequently has little effect on estimator quality. We also examine one of Ait-Sahalia's [1996a] new nonparametric tests of parametric continuous-time Markov models of the instantaneous spot interest rate. The test is based on the distance between parametric and nonparametric (kernel) estimates of the ergodic distribution of the interest rate process. Our principal result is that the test rejects too often when using asymptotic critical values and 22 years of data. The reason for the high rejection rate is probably because the asymptotic distribution of the test does not depend on persistence, but the finite sample performance of the estimator does. After critical values are adjusted for size, the test has low power in distinguishing between the Vasicek and Cox-Ingersoll- Ross models when compared with a conditional moment based specification test.

Full paper (2045 KB Postscript)

Keywords: Interest rate, nonparametric, bandwidth, specification test

PDF: Full Paper

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