Poisson–geometric INAR(1) process for modeling count time series with overdispersion

In this paper, we propose a new first‐order non‐negative integer‐valued autoregressive [INAR(1)] process with Poisson–geometric marginals based on binomial thinning for modeling integer‐valued time series with overdispersion. Also, the new process has, as a particular case, the Poisson INAR(1) and geometric INAR(1) processes. The main properties of the model are derived, such as probability generating function, moments, conditional distribution, higher‐order moments, and jumps. Estimators for the parameters of process are proposed, and their asymptotic properties are established. Some numerical results of the estimators are presented with a discussion of the obtained results. Applications to two real data sets are given to show the potentiality of the new process.