Zero truncated Poisson integer-valued AR(1) model

In this paper, we introduce a new stationary integer-valued autoregressive process of the first order with zero truncated Poisson marginal distribution. We consider some properties of this process, such as autocorrelations, spectral density and multi-step ahead conditional expectation, variance and probability generating function. Stationary solution and its uniqueness are obtained with a discussion to strict stationarity and ergodicity of such process. We estimate the unknown parameters by using conditional least squares estimation, nonparametric estimation and maximum likelihood estimation. The asymptotic properties and asymptotic distributions of the conditional least squares estimators have been investigated. Some numerical results of the estimators are presented and some sample paths of the process are illustrated. Some possible applications of the introduced model are discussed.