The Bickel–Rosenblatt test for diffusion processes

Abstract: 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. [Copyright &y& Elsevier]