Abstract
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.
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