Estimation for change point of discretely observed ergodic diffusion processes

TL;DR

This paper develops methods to estimate the timing of change points in discretely observed ergodic diffusion processes, providing convergence rates and distributional results, with applications demonstrated through examples and simulations.

Contribution

It introduces novel estimators for change points in ergodic diffusion processes and analyzes their convergence and distributional properties.

Findings

Proposed estimators have established rates of convergence.

Distributional limits of the estimators are derived.

Simulation results support theoretical findings.

Abstract

We treat the change point problem in ergodic diffusion processes from discrete observations. Tonaki et al. (2020) proposed adaptive tests for detecting changes in the diffusion and drift parameters in ergodic diffusion models. When any changes are detected by this method, the next question to be considered is where the change point is. Therefore, we propose the method to estimate the change point of the parameter for two cases: the case where there is a change in the diffusion parameter, and the case where there is no change in the diffusion parameter but a change in the drift parameter. Furthermore, we present rates of convergence and distributional results of the change point estimators. Some examples and simulation results are also given.