Iranian Statistical Society Journal of the Iranian Statistical Society 1726-4057 11 2 2022 07 23 Integer Valued AR(1) with Geometric Innovations مدل AR صحیح مقدار با تغییرات هندسی 173 190 253688 EN Mansour Aghababaei Jazi Geoff Jones Chin-Diew Lai Journal Article 2022 07 23 The classical integer valued first-order autoregressive (INA- R(1)) model has been defined on the basis of Poisson innovations. This model has Poisson marginal distribution and is suitable for modeling equidispersed count data. In this paper, we introduce an modification of the INAR(1) model with geometric innovations (INARG(1)) for model- ing overdispersed count data. We discuss some structural mathematical properties of the process comparing with classical INAR(1). Also, the superiority of the model in contrast with the INAR(1) is shown by some real time series. Binomial thinning operator conditional maximum likeli- hood estimation infinitely divisible distributions mixture distributions https://jirss.irstat.ir/article_253688_fe142115b95dbd049f5075ccd24ce1ad.pdf