Parameter Estimation Of The First Order Integer-valued Autoregressive Model With ZIP Innovation Term

In practical projects,people usually use INAR(1)model which based on thin-ning operator to research it for analysing time series count data reasonably.But,the previous INAR(1)model may not be suitable for it when there are excess zeros.This paper builds the INAR(1)model with ZIP(Zero-inflated Poisson)innova-tion term for researching the time series count data with excess zeros.Based on the consideration of the effect of the independent variable on the response variable,this paper introduces the classic ZIP regressive model in the part of innovation term.This paper also discusses two INNAR(1)models based on binomial thinning operator and negative binomial thinning operator,and researches the problem of parameter estima-tion based on the conditional maximum likelihood estimate(CML).In addition,we introduce random effects in the part of ZIP regression for the research of the hetero-geneity from different individuals,and study those models' parameter estimation by non-parametric estimate and MCMC algorithm.Based on the given methods,this pa-per analyses the effect of parameter estimation by lots of stochastic simulation,and finds that the CML estimate is appropriate and effective for the basic INAR(l)mod-el.And for the INAR(1)model with random effects,the size of variance of random effects has some influence on the estimation of two methods,but the final result is acceptable when the size is comparatively large.In the end,it is further explained that the related method in this paper is effective by the fitting analysis of silverleaf whitefly data.