Estimation of multiple change points under a generalised Ornstein-Uhlenbeck framework

TL;DR

This paper develops new statistical methods to detect multiple change points in a generalized Ornstein-Uhlenbeck process, which models mean-reverting financial data, providing consistent estimators and practical algorithms for real-world applications.

Contribution

It introduces two novel estimation methods for multiple change points in a generalized OU model, with proven asymptotic properties and algorithms for implementation.

Findings

Methods accurately detect change points in simulated data.

Algorithms successfully applied to real financial market data.

Estimation procedures are consistent and theoretically justified.

Abstract

The use of an Ornstein-Uhlenbeck (OU) process is ubiquitous in business, economics and finance to capture various price processes and evolution of economic indicators exhibiting mean-reverting properties. When structural changes happen, economic dynamics drastically change and the times at which these occur are of particular interest to policy makers, investors and financial product providers. This paper addresses the change-point problem under a generalised OU model and investigates the associated statistical inference. We propose two estimation methods to locate multiple change points and show the asymptotic properties of the estimators. An informational approach is employed in detecting the change points, and the consistency of our methods is also theoretically demonstrated. Estimation is considered under the setting where both the number and location of change points are unknown. Three computing algorithms are further developed for implementation. The practical applicability of our methods is illustrated using simulated and observed financial market data.