A Two-Step Test for the Two-Sample Problem of Processes of Ornstein-Uhlenbeck Type

The authors propose a two-step test for the two-sample problem of processes of Ornstein-Uhlenbeck type. In the first step, the authors test the equality of correlation structures, based on the least square estimators of the correlation parameters, and the test statistic follows the standard normal distribution. If the null hypothesis is not rejected in the first step, the authors consider a second step to test the equality of marginal distributions, based on the weighted deviation of the empirical characteristic functions; the test statistic has a complicated asymptotic distribution, so that sequential bootstrap method is applied to reach a temporary decision. Simulation studies and real data analysis suggest that the proposed approach performs well in finite samples.