First-order mixed integer-valued autoregressive processes with zero-inflated generalized power series innovations

To model zero-inflated time series of counts, we propose a first-order mixed integer-valued autoregressive process with zero-inflated generalized power series innovations. These innovations contain the commonly used zero-inflated Poisson and geometric distributions. Strict stationarity, ergodicity of the process, and some important probabilistic properties such as the transition probabilities, the kk-step ahead conditional mean and variance are obtained. The conditional maximum likelihood estimators for the parameters in this process are derived and the performances of the estimators are studied via simulation. As illustration, an application to an offence data set is given to show the effectiveness of the proposed model.