A Test for Model Specification of Diffusion Processes

This paper evaluates the use of the nonparametric kernel method for testing specification of diffusion models as originally considered in Aı̈t-Sahalia (1996). A serious doubt on the ability of the kernel method for diffusion model testing has been cast in Pritsker (1998), who observes severe size distortion of the test proposed by Aı̈t-Sahalia and finds that 2755 years of data are required in order for the kernel density estimator to attain a level of accuracy achieved with 22 years of independent data. We introduce in this paper a set of measures to formulate a new test based on the kernel method and show that the severe size distortion observed by Pritsker (1998) can be overcome. The meaures include targeting at the transitional desnity of the process, using the empirical likelihood to formulate the test statistics, properly smoothing of model-implied transtional densities and employing a parametric bootstrap procedure in approximating the distribution of test statistics. Our simulation for both the Vasicek and Cox-Ingersoll-Ross diffusion models indicates that the proposed test has reasonable size and power under various degrees of data dependence for as little as 10 years of data. We then apply the proposed test to a monthly Federal Fund rate data and find that there is some empirical support for several of the one-factor diffusion models proposed in the literature.