Detecting multiple change points in linear models with heteroscedastic errors

2025-05-02

AI Summary

This paper addresses the detection of multiple change points in regression parameters of linear regression models under heteroscedastic errors. To handle complex settings—including weak dependence, nonstationarity, and abrupt or gradual variance changes—we develop a weighted residual CUSUM process framework. We establish, for the first time, the asymptotic theory for multiple change-point testing under joint heteroscedasticity, weak dependence, and nonstationarity of errors. Furthermore, we propose a finite-sample correction method that substantially improves Type I error control and change-point localization accuracy. Simulation studies and empirical applications—spanning predictive regression and asset pricing—demonstrate that the proposed method robustly identifies multiple parameter breaks with low false discovery rates, and consistently outperforms conventional homoscedasticity-based approaches.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

The problem of detecting change points in the regression 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.

Problem

• Detecting change points in linear models with heteroscedastic errors
• Adapting CUSUM tests for non-stationary, weakly dependent errors
• Controlling Type I error in heteroscedastic regression change detection

Innovation

• Weighted CUSUM processes for heteroscedastic errors
• Adapted change-point tests for linear models
• Finite sample adjustment for testing procedures