The Bickel-Rosenblatt test for diffusion processes

In this paper, we consider the Bickel-Rosenblatt test for a class of diffusion processes that covers the Ornstein-Uhlenbeck process. Using the discrete sampling scheme, we calculate residuals and construct the residual based Bickel-Rosenblatt test. We show that the test statistic is asymptotically normal under regularity conditions. The result is applicable to the test for the existence of jumps in diffusion models.