A Simulation Test for Continuous-Time Models

In this article, we propose a simulation method to implement Hong and Li’s (2005) transition density based test for continuous-time models. The idea is to simulate a sequence of dynamic probability integral transforms, which is the key ingredient of Hong and Li’s (2005) test. The proposed procedure is generally applicable no matter whether or not the transition density of a continuous-time model has a closed form, and is simple and computationally inexpensive. A Monte Carlo study shows that the proposed simulation test has very similar sizes and powers to Hong and Li’s (2005) test using the closed form of the transition density (when available). Furthermore, the performance of the simulation test is robust to the choice of the number of simulation iterations and the number of discretization steps between adjacent observations.