Some geometric mixed integer-valued autoregressive (INAR) models

In this paper, we introduce some mixed integer-valued autoregressive models of orders 1 and 2 with geometric marginal distributions, denoted by MGINAR(1) and MGINAR(2), using a mixture of the well-known binomial and the negative binomial thinning. The distributions of the innovation processes are derived and several properties of the model are discussed. Conditional least squares and Yule-Walker estimators are obtained, and some numerical results of the estimations are presented. A real-life data example is investigated to assess the performance of the models. (C) 2012 Elsevier B.V. All rights reserved.