Parameter change test for location‐scale time series models with heteroscedasticity based on bootstrap

Abstract

This study considers the bootstrap cumulative sum (CUSUM) test for a parameter change in location‐scale time series models with heteroscedasticity. The CUSUM test has been popular for detecting an abrupt change in time series models because it performs well in many applications. However, it has severe size distortions in many situations. As a remedy, we consider the bootstrap CUSUM test, particularly focusing on the CUSUM test based on score vectors, and demonstrate the weak consistency of the bootstrap test for its justification. A simulation study and data analysis are conducted for illustration.