Change point inference in ergodic diffusion processes based on high frequency data

We deal with the change point problem in ergodic diffusion processes based on high frequency data. Tonaki et al. (2020, 2021) studied the change point problem for the ergodic diffusion process model. However, the change point problem for the drift parameter when the diffusion parameter changes is still open. Therefore, we consider the change detection and the change point estimation for the drift parameter taking into account that there is a change point in the diffusion parameter. Moreover, we examine the performance of the tests and the estimation with numerical simulations.