A study on mixed poisson integer-valued times series models

Abstract

In 2017, Batteto-Souza extended the Poisson INAR(1) to the Mixed Poisson INAR(1) model to accommodate overdispersion data. In Their study, they considered the Poisson inverse-gaussian INAR(1) model. In this project, we will extend the study of the Mixed Poisson INAR(1) model to construct a Mixed Poisson INMA(q) model and derive their probabilistic properties such as mean, variance and covariance. Moreover, we present distribution plots of such data in many different settings.