Modeling and inference for counts time series based on zero-inflated exponential family INGARCH models

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 family (ZIEF) INGARCH process is stationary ergoic, maximum likelihood estimator consistent asymptotically normal. then construct CUSUM based on (standardized) residuals squares test. Their null distributions shown to converge sup Brownian bridge in distribution. The validity confirmed through simulation real data analysis.