Some estimation and forecasting procedures in Possion-Lindley INAR(1) process

Abstract

We study the estimation and forecasting in first-order integer-valued autoregressive process with Poisson-Lindley (PLINAR(1)) marginal distribution (Mohammadpour et al.). Quasi-likelihood estimators are proposed for the parameters of interest and their asymptotic properties are derived. Two methods for coherent point prediction are given and the prediction intervals for future data are constructed. We present some simulations to verify rationality of the proposed estimation and prediction methods. An application to a real data about animal’s anorexia is also provided.