Periodic integer-valued GARCH(1, 1) model

This article deals with some probabilistic and statistical properties of a periodic integer-valued GARCH(1,1) model. Necessary and sufficient conditions for the periodical stationary, both in mean and second order, are established. The closed-forms of the mean and the second moment are, under these conditions, obtained. The condition of the existence of higher moment orders and their explicit formula in terms of the parameters are established. The autocovariance structure is studied, while providing the closed-form of the periodic autocorrelation function. The Yule–Walker and the likelihood estimations of the underlying parameters are obtained. A simulation study and an application on real dataset are provided.