A combined geometric INAR(p) model based on negative binomial thinning

In this paper, we introduce a new (combined) integer‐valued autoregressive model of order $p$ with geometric marginal distributions, denoted by CGINAR( $p$ ), using the negative binomial thinning introduced by Ristic et al. . Several properties of the model are constructed and discussed, including one‐step ahead conditional statistical measures. Some methods for estimating the model parameters are considered and the asymptotic properties of the obtained estimators are derived. A real‐life data example is investigated to assess the performance of the model.