We develop a nonparametric specification test for continuous-time models using the transition density. Using a data transform and correcting for the boundary bias of kernel estimators, our test is robust to serial dependence in data and provides excellent finite sample performance. Besides univariate diffusion models, our test is applicable to a wide variety of continuous-time and discrete-time dynamic models, including time-inhomogeneous diffusion, GARCH, stochastic volatility, regime-switching, jump-diffusion, and multivariate diffusion models. A class of separate inference procedures is also proposed to help gauge possible sources of model mis-specification. We strongly reject a variety of univariate diffusion models for daily Eurodollar spot rates and some popular multivariate affine term structure models for monthly U.S. Treasury yields.

We develop a nonparametric specification test for continuous-time models using the transition density. Using a data transform and correcting for the boundary bias of kernel estimators, our test is robust to serial dependence in data and provides excellent finite sample performance. Besides univariate diffusion models, our test is applicable to a wide variety of continuous-time and discrete-time dynamic models, including time-inhomogeneous diffusion, GARCH, stochastic volatility, regime-switching, jump-diffusion, and multivariate diffusion models. A class of separate inference procedures is also proposed to help gauge possible sources of model misspecification. We strongly reject a variety of univariate diffusion models for daily Eurodollar spot rates and some popular multivariate affine term structure models for monthly U.S. Treasury yields.