Inferential aspects of the zero-inflated Poisson INAR(1) process

Abstract

• Provide Yule–Walker and two-step Conditional Least Squares estimation methods. • Comparison with the Conditional Maximum Likelihood approach under misspecification. • Obtain the asymptotic distribution of the Yule–Walker estimators. • Two real count time series data are analysed based on our methodology. A first-order INteger-valued AutoRegressive (INAR) process with zero-inflated Poisson distributed innovations was proposed by Jazi, Jones and Lai (2012) [First-order integer valued AR processes with zero inflated Poisson innovations. Journal of Time Series Analysis. 33, 954–963.] , which is able for dealing with zero-inflated/deflated count time series data. The inferential aspects of this model were not well explored by the authors, only a conditional maximum likelihood approach was briefly discussed. In this paper, we explore the inferential aspects of this zero-inflated Poisson INAR(1) process. We propose parameter estimation through Two-Step Conditional Least Squares and Yule–Walker methods. The asymptotic properties of the estimators are provided. Simulation results about the finite-sample behavior of both estimation methods and comparisons with the conditional maximum likelihood approach are presented under correct model specification and misspecification. Two empirical applications to real data sets are considered in order to illustrate the usefulness of the proposed methodology in practical situations.