A Non-Parametric Test for Continuous-Time Homogeneous Markov Process: Is It a Diffusion Process?
چکیده
This paper proposes a nonparametric method to test whether an underlying continuoustime homogeneous Markov process is a diffusion process. The test statistic is based on the infinitesimal generator. Under the null hypothesis, we show that the limit distribution of the test statistic is normal. Under the alternative hypothesis, where the jump-diffusion process is assumed, the power of the test is shown to converge to one in probability. The test can also detect local alternatives which converge to the null at certain rate. Monte-Carlo simulations are conducted to show how the test behaves under the null and alternative hypothesis for finite samples, we also apply our test to some high frequency empirical time series data to see whether they follow diffusions or not.