QMLE of periodic integer-valued time series models

Abstract

In this paper, we establish the consistency and the asymptotic normality of the Periodic Poisson (respectively the Periodic Geometric) Quasi Maximum Likelihood estimators, (respectively , of a general class of periodic count time series models. In this class, the conditional mean is expressed as a parametric and measurable function, with periodic parameters, of the infinite past of the observed process. Applications for some particular periodic models of the class of Periodic Integer-Valued Autoregressive Moving Average, (PINARMA) models, are, under some regularity conditions, considered. The performances of these considered estimation methods are assisted by an intensive simulation study. Moreover, applications on two real datasets are provided.