Zero-inflated Poisson INAR(1) model with periodic structure

The modeling of integer-valued time series has received considerable attention, which has led to the introduction and in-depth study of various linear models to develop appropriate ones for such data. Among these models, the integer-valued autoregressive INAR model has been particularly prominent. However, this model fails to take adequate account of the periodic feature in the datasets. To address this limitation, we propose a new model in this article: the periodic integer-valued autoregressive model with a zero-inflated Poisson distribution innovation PZIP-INAR(1). This model effectively captures the overdispersion resulting from an excessive number of zeros in periodic cases. Indeed, we provide clear definitions of the model and establish the periodic stationarity conditions. In addition, we derive explicit expressions for the periodic mean, variance, and autocovariance structure of the proposed model. The estimation problem is addressed via three different methods. The performance of these methods is thoroughly evaluated through intensive simulation studies and an application of real data by analyzing the daily number of COVID-19 deaths in Finland.