PREDICTION MEAN SQUARED ERROR OF THE POISSON INAR(1) PROCESSWITH ESTIMATED PARAMETERS

Abstract

Recently, as a result of the growing interest in modeling stationary pro-cesses with discrete marginal distributions, several models for integer valuedtime series have been proposed in the literature. One of these models isthe integer-valued autoregressive (INAR) models. However, when modelingwith integer-valued autoregressive processes, the distributional propertiesof forecasts have been not yet discovered due to the diculty in handlingthe Steutal Van Harn thinning operator \ "(Steutal and van Harn, 1979).In this study, we derive the mean squared error ofh-step-ahead predictionfrom a Poisson INAR(1) process, reecting the eect of the variability ofparameter estimates in the prediction mean squared error.AMS 2000 subject classications.Primary 60G10; Secondary 37M10.Keywords.Stationary process, integer valued time series, mean-squared pre-diction errors.1. IntroductionThere has been a growing research in modeling discrete time stationary pro-cesses with discrete marginal distributions. The usual linear models for timeseries, ARMA models, are suitable for modeling stationary dependent sequencesunder the Gaussian assumption. However, the Gaussian assumption is often inap-propriate for modeling counting data. Thus, motivated by the need for modelingcorrelated series of counts, several models for integer-valued time series have beenproposed in the literature.Received January 2006; accepted February 2006.1Corresponding author. Institute of Statistics, Korea University, Seoul 136-701, Korea (e-mail : starkim@korea.ac.kr)