A Simulation Based Specification Test for Diffusion Processes

This paper makes two contributions. First, we outline a simple simulation based framework for constructing conditional distributions for multi-factor and multi-dimensional diffusion processes, for the case where the functional form of the conditional density is unknown. The distributions can be used, for example, to form predictive confidence intervals for time period t Tau , given information up to period t. Second, we use the simulation based approach to construct a test for the correct specification of a diffusion process. The suggested test is in the spirit of the conditional Kolmogorov test of Andrews (1997). However, in the present context the null conditional distribution is unknown and is replaced by its simulated counterpart. The limiting distribution of the test statistic is not nuisance parameter free. In light of this, symptotically valid critical values are obtained via appropriate use of the block bootstrap. The suggested test has power against a larger class of alternatives than tests that are constructed using marginal distributions/densities, such as those in Ait-Sahalia (1996) and Corradi and Swanson (2005a). The findings of a small Monte Carlo experiment underscore the good finite sample properties of the proposed test, and an empirical illustration underscores the ease with which the proposed simulation and testing methodology can be applied