In this article, a new kind of stationary zero-inflated Pegram’s operator based integer-valued time series process of order p with Poisson marginal or ZIPPAR(p) process is constructed for modelling count time series consisting a large number of zeros compared to standard Poisson time series processes. Several properties like stationarity, ergodicity are examined. Estimates of the model parameters are studied using three methods of estimation, namely Yule–Walker, conditional least squares and maximum likelihood estimation. Also h-step ahead coherent forecasting distributions of the proposed process for p = 1, 2 are derived. Real data set is used to examine and illustrate the proposed process with some simulation studies.
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