Page's Sequential Procedure for Change-Point Detection in Time Series Regression

TL;DR

This paper introduces modified CUSUM procedures for detecting change-points in regression parameters of multiple time series, offering improved stability over traditional methods, with proven asymptotic properties and demonstrated effectiveness in financial data analysis.

Contribution

The paper develops and analyzes modified CUSUM procedures that are more stable for late change detection in multiple time series regression models.

Findings

Modified procedures show higher stability for late changes.

Asymptotic distributions and consistency are established.

Procedures perform well in finite sample simulations.

Abstract

In a variety of different settings cumulative sum (CUSUM) procedures have been applied for the sequential detection of structural breaks in the parameters of stochastic models. Yet their performance depends strongly on the time of change and is best under early-change scenarios. For later changes their finite sample behavior is rather questionable. We therefore propose modified CUSUM procedures for the detection of abrupt changes in the regression parameter of multiple time series regression models, that show a higher stability with respect to the time of change than ordinary CUSUM procedures. The asymptotic distributions of the test statistics and the consistency of the procedures are provided. In a simulation study it is shown that the proposed procedures behave well in finite samples. Finally the procedures are applied to a set of capital asset pricing data related to the Fama-French extension of the capital asset pricing model.