Detecting multiple change points in linear models with heteroscedasticity

TL;DR

This paper develops and evaluates methods for detecting multiple change points in linear regression models with heteroscedastic errors, providing theoretical insights and practical tools for identifying parameter instability under complex variance structures.

Contribution

It introduces asymptotic results and adapted test statistics for change point detection in heteroscedastic linear models, supported by simulation and real data applications.

Findings

Methods effectively detect multiple change points in heteroscedastic settings.

Proposed tests control Type I error rate under non-stationary variance.

Applications demonstrate usefulness in financial and predictive modeling.

Abstract

The problem of detecting change points in the parameters of a linear regression model with errors and covariates exhibiting heteroscedasticity is considered. Asymptotic results for weighted functionals of the cumulative sum (CUSUM) processes of model residuals are established when the model errors are weakly dependent and non-stationary, allowing for either abrupt or smooth changes in their variance. These theoretical results illuminate how to adapt standard change point test statistics for linear models to this setting. We studied such adapted change-point tests in simulation experiments, along with a finite sample adjustment to the proposed testing procedures. The results suggest that these methods perform well in practice for detecting multiple change points in the linear model parameters and controlling the Type I error rate in the presence of heteroscedasticity. We illustrate the use of these approaches in applications to test for instability in predictive regression models and explanatory asset pricing models.