On Periodic Generalized Poisson INAR(1) Model

Abstract

In this paper, we introduce a first-order Periodic Generalized Poisson Integer-Valued Autoregressive model which has been shown to be useful to describe overdispersion, equidispersion and underdispersion feature encountered in periodically correlated Integer-Valued time series. Some probabilistic and statistical properties are established, such as the periodically correlated stationarity conditions, in the first and the second moments are provided and the closed-forms of these moments are, under these conditions, derived. Moreover, the structure of the periodic autocovariance is obtained. The estimation problem is addressed through the Yule-Walker the Two-Stage Conditional Least Squares and the Conditional Maximum Likelihood methods. The performance of these methods is done through an intensive simulation study and an application on real data set is accomplished. Keywords and phrases: Periodic Generalized Poisson, Integer-Valued Autoregressive, Periodically correlated process, periodically stationary condition.