Extended Poisson INAR(1) processes with equidispersion, underdispersion and overdispersion

Abstract

Real count data time series often show the phenomenon of the underdispersion\nand overdispersion. In this paper, we develop two extensions of the first-order\ninteger-valued autoregressive process with Poisson innovations, based on\nbinomial thinning, for modeling integer-valued time series with equidispersion,\nunderdispersion and overdispersion. The main properties of the models are\nderived. The methods of conditional maximum likelihood, Yule-Walker and\nconditional least squares are used for estimating the parameters, and their\nasymptotic properties are established. We also use a test based on our\nprocesses for checking if the count time series considered is overdispersed or\nunderdispersed. The proposed models are fitted to time series of number of\nweekly sales and of cases of family violence illustrating its capabilities in\nchallenging cases of overdispersed and underdispersed count data.\n