Change Point Testing for the Drift Parameters of a Periodic Mean Reversion Process

TL;DR

This paper develops a statistical test to detect changes in the drift parameters of a periodic mean reversion process modeled as a generalized Ornstein-Uhlenbeck process, with explicit formulas and asymptotic analysis.

Contribution

It provides an explicit likelihood ratio test for change points in the drift of a periodic mean reversion process, including asymptotic distribution under the null hypothesis.

Findings

Derived explicit likelihood ratio test statistic.

Determined asymptotic distribution under null hypothesis.

Applicable to continuous-time observed processes.

Abstract

In this paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein-Uhlenbeck process which is defined as the solution of $dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t$, and which is observed in continuous time. We derive an explicit representation of the generalized likelihood ratio test statistic assuming that the mean reversion function $L(t)$ is a finite linear combination of known basis functions. In the case of a periodic mean reversion function, we determine the asymptotic distribution of the test statistic under the null hypothesis.