Change-Point Detection in Time Series Using Mixed Integer Programming

TL;DR

This paper introduces a mixed integer programming approach for detecting and estimating multiple structural breaks in time series regression models, offering a more accurate and flexible alternative to traditional methods.

Contribution

The paper develops a novel MIO-based framework that jointly estimates the number, location of breaks, and regression coefficients, outperforming classical methods.

Findings

MIO finds provably optimal solutions for change-point detection.

The framework outperforms LASSO and classical methods in accuracy.

Empirical examples demonstrate practical usefulness in economics and business.

Abstract

We use cutting-edge mixed integer optimization (MIO) methods to develop a framework for detection and estimation of structural breaks in time series regression models. The framework is constructed based on the least squares problem subject to a penalty on the number of breakpoints. We restate the $l_0$-penalized regression problem as a quadratic programming problem with integer- and real-valued arguments and show that MIO is capable of finding provably optimal solutions using a well-known optimization solver. Compared to the popular $l_1$-penalized regression (LASSO) and other classical methods, the MIO framework permits simultaneous estimation of the number and location of structural breaks as well as regression coefficients, while accommodating the option of specifying a given or minimal number of breaks. We derive the asymptotic properties of the estimator and demonstrate its effectiveness through extensive numerical experiments, confirming a more accurate estimation of multiple breaks as compared to popular non-MIO alternatives. Two empirical examples demonstrate usefulness of the framework in applications from business and economic statistics.