The Statistical Inference Of Integer-Valued Autoregressive Processes With Missing Data

Recently, many authors are becoming more and more interested in mod-eling time-series models for count data, but this kind of data from evidence are often missed. It is inaccurate to use the incomplete data for research of statistical inference. In this article, to solve this problem, we review and dis-cuss the methods for estimating the parameters of interest in integer-valued autoregressive models in the presence of missing data.Firstly, we introduce the definition, distribution properties and parame-ter estimation of INAR(1) model, then give a brief description of INAR(p) model. Secondly, we summarize the methods for dealing with missing data in INAR(1) model. The methods are divided into two classes which include delete method and replace method. We explain the ideas and applications of various methods in details. Simulation comparisons are reported for Poisson INAR(1) model. It is noted that we propose EM imputation for Poisson INAR(1) model with missing data and extend some of above methods to Poisson INAR(p) model.