This study considers statistical inferences such as parameter estimation and change tests for counts time series models where the conditional density of present observations over past information follow a zero-inflated one-parameter exponential family. We verify that the zero-inflated exponential family (ZIEF) INGARCH process is stationary and ergoic, and the maximum likelihood estimator is consistent and asymptotically normal. We then construct CUSUM tests based on (standardized) residuals and squares of (standardized) residuals as a parameter change test. Their null distributions is shown to converge to the sup of a Brownian bridge in distribution. The validity of the CUSUM tests is confirmed through a simulation study and real data analysis.

本研究考虑了统计推断，例如计数时间序列模型的参数估计和变化测试，其中当前观测值相对于过去信息的条件密度遵循零膨胀的单参数指数族。我们验证了零膨胀指数族 (ZIEF) INGARCH 过程是平稳且能效的，并且最大似然估计量是一致且渐近正态的。然后，我们基于（标准化）残差和（标准化）残差的平方构建 CUSUM 测试作为参数变化测试。显示它们的零分布收敛到分布中的布朗桥的 sup。CUSUM 测试的有效性通过模拟研究和实际数据分析得到证实。