Nonparametric Specification Testing for Continuous-Time Models with Application to Spot Interest Rates

Abstract

We propose two nonparametric transition density-based speciÞcation tests for continuous-time diffusion models. In contrast to marginal density as used in the literature, transition density can capture the full dynamics of a diffusion process, and in particular, can distinguish processes with the same marginal density but different transition densities. To address the concerns of the Þnite sample performance of nonparametric methods in the literature, we introduce an appropriate data transformation and correct the boundary bias of kernel estimators. As a result, our tests are robust to persistent dependence in data and provide reliable inferences for sample sizes often encountered in empirical Þnance. Simulation studies show that our tests have reasonable size and good power against a variety of alternatives in Þnite samples even for data with highly persistent dependence. Besides the single-factor diffusion models, our tests can be applied to a broad class of dynamic economic models, such as discrete time series models, time-inhomogeneous diffusion models, stochastic volatility models, jump-diffusion models, and multi-factor term structure models. When applied to daily Eurodollar interest rates, our tests overwhelmingly reject some popular spot rate models, including those with nonlinear drifts that some existing tests can not reject after correcting size distortions. We Þnd that models with nonlinear drifts do not signiÞcantly improve the goodness-of-Þt, and the main source of model inadequacy seems to be the violation of the Markov assumption. We also Þnd that GARCH, regime switching and jump diffusion models perform signiÞcantly better than single-factor diffusion models, although they are far from being adequate to fully capture the interest rate dynamics. Our study shows that nonparametric methods are a reliable and powerful tool for analyzing Þnancial data.