Title: Detecting change points in linear models with homoscedastic or heteroscedastic errors
Authors: Lajos Horvath - University of Utah (United States)
Gregory Rice - University of Waterloo (Canada)
Yuqian Zhao - University of Essex (United Kingdom) [presenting]
Abstract: The problem of detecting change points in the regression parameters of a standard linear model is considered. Motivated by statistics arising from maximally selected likelihood ratio tests, we provide a comprehensive asymptotic theory for weighted functionals of the cumulative sum (CUSUM) process of the residuals, which includes most statistics used for this problem to date. Asymptotic results of this type are then extended to the setting when the model errors and/or covariates exhibit heteroscedasticity. These theoretical results illuminate how to adapt standard change point test statistics to this situation. Such adaptations are studied in a simulation study along with a method based on a classical approximation to improve the finite sample performance of these tests, which show that they work well in practice to detect multiple change points in the linear model parameters, and control the Type-I testing error in the presence of heteroscedasticity. The proposed methods are illustrated with applications to financial sentiment analysis, and to measure for changes in the relationship between COVID-19 infections and deaths in the United Kingdom.