Recent progress in parameter change test for integer-valued time series models

In this study, we review a recent progress regarding the change point test for integer-valued time series models, specifically concentrating on the CUSUM test for integer-valued autoregressive (INAR) and generalized autoregressive conditional heteroscedastic (INGARCH) models. Because time series often experience changes in underlying models, the change point test has been a fundamental issue in time series analysis during the past decades. We first introduce the CUSUM test in a general set-up and then construct estimate-, score vector- and residual-based CUSUM tests in INAR and INGARCH models and state their limiting null distributions. Finally, the residual-based CUSUM of squares test and the robust change point test based on the density power divergence are addressed.