Determination of a structural break in a mean-reverting process

TL;DR

This paper introduces two statistically consistent methods for detecting change points in mean-reverting processes, specifically within a generalized Ornstein-Uhlenbeck model, and compares their effectiveness through numerical tests.

Contribution

It demonstrates the equivalence of least squares and maximum likelihood methods for change point detection in a generalized Ornstein-Uhlenbeck process, including unknown change point scenarios.

Findings

Methods are consistent in locating change points.

Numerical illustrations show comparable performance of both methods.

Approach effectively handles unknown change point cases.

Abstract

Determining accurately when regime and structural changes occur in various time-series data is critical in many social and natural sciences. We develop and show further the equivalence of two consistent estimation techniques in locating the change point under the framework of a generalised version of the Ornstein-Uhlehnbeck process. Our methods are based on the least sum of squared error and the maximum log-likelihood approaches. The case where both the existence and the location of the change point are unknown is investigated and an informational methodology is employed to address these issues. Numerical illustrations are presented to assess the performance of the methods.