Estimation And Forecasting Procedures For INAR(1) Processes

We consider the estimation and forecasting procedures for two types of first-order integer-valued autoregressive processes.First,we study the first-order integer-valued autoregressive process with Poisson-Lindley marginal distribution.Weighed conditional least squared 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.Second,we propose the weighed conditional least squares estimators for the parameters of interest in the INAR(1)model with dependent counting series.Some asymptotic results of the proposed estimators are established.We present the higher-order moments,higher-order cumulants,spectral and bispectral density functions.To assess the performance of the weighed conditional least squares,we compare it with conditional least squares and Yule-Walker via numerical simulation.