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

Abstract

We propose two nonparametric specification tests for continuous-time models based on transition density, which unlike the marginal density used in the literature, can capture the full dynamics of a continuous-time process. To improve the finite sample performance of nonparametric methods, we introduce a 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 finance. Simulation studies show that even for data with highly persistent dependence, our tests have reasonable size and good power against a variety of alternatives in finite samples. Besides one-factor diffusion models, our tests can also be applied to a broad class of dynamic models, including discrete-time dynamic models, time-inhomogeneous diffusion models, stochastic volatility models, jump-diffusion models,and multi-factor diffusion models. When applied to Eurodollar interest rates, our tests overwhelmingly reject a variety of existing popular one-factor diffusion models. We find that introducing a nonlinear drift does not significantly improve the goodness of fit, and the main reason for the rejection of one-factor diffusion models is the violation of the Markov assumption. Some existing popular non-Markovian models with GARCH, regime switching and jumps significantly outperform one-factor diffusion models, but they are still far from being adequate to fully capture the interest rate dynamics. Our study shows that contrary to the general perception in the literature, nonparametric methods can be a reliable and powerful tool for analyzing financial data.