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.

在这项研究中，我们回顾了有关整数值时间序列模型的更改点检验的最新进展，特别是针对整数值自回归（INAR）和广义自回归条件异方差（INGARCH）模型的CUSUM检验。由于时间序列经常会经历基础模型的更改，因此在过去的几十年中，更改点测试一直是时间序列分析中的一个基本问题。我们首先在一般设置中介绍CUSUM检验，然后在INAR和INGARCH模型中构造基于估计，得分向量和残差的CUSUM检验，并说明其极限零分布。最后，讨论了基于残差的平方CUSUM检验和基于密度幂散的鲁棒变化点检验。