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

TL;DR

This paper addresses the challenge of detecting and estimating change points in the drift parameter of ergodic diffusion processes using high frequency data, considering simultaneous changes in diffusion parameters.

Contribution

It introduces methods for change detection and estimation of the drift parameter accounting for diffusion parameter changes, extending prior work.

Findings

Proposed new change point detection methods for ergodic diffusions.

Numerical simulations demonstrate the effectiveness of the methods.

The approach handles simultaneous changes in drift and diffusion parameters.

Abstract

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.