A first-order integer-valued autoregressive process with zero-modified Poisson-Lindley distributed innovations

Abstract

In this paper, we introduce a first-order integer-valued autoregressive process with zero-modified Poisson-Lindley distributed innovations based on the binomial thinning operator. Some statistical and conditional properties of the model are presented, several estimation methods are applied to estimate the unknown parameters and, for the Yule-Walker and conditional least square estimators, the asymptotic distributions are obtained. Besides, a simulation study is conducted to compare the performance of the proposed estimators and, finally, two real count time series data are applied to demonstrate the usefulness of the proposed model.