Stationarity Test For Poisson Autoregressive Model

In recent years,there has been growing interest in studying the problems of the modeling and statistical inference for integer-valued time series.Many integer-valued random variables are approximate to Poisson distribution.Therefore some Poisson autoregressive models were established to fit this circumstance.When we fit the actual observation data,we must test whether the data are stationary at first.Previous literature on Poisson autoregressive model,only gave the estimation method of parameters and the stationary condition of model.However,there is no method to study the stationary test for Poisson autoregressive model.In this article,we come to study the stability test problem of Poisson autoregressive model.Firstly,we introduce the background and current investigation situation of Poisson distribution,Poisson regression model and empirical Likelihood method.Secondly,we are concerned with the Poisson autoregressive model and discuss its properties.Moreover,we also establish the test statistic to test the stability of Poisson autoregressive model.The study utilized the least squares method to estimate the parameters in the model and established nonparametric empirical Likelihood ratio statistic by using the empirical Likelihood method.We proved the limiting distribution of test statistic by using the ergodicity theorem,law of large numbers and central limit theorem Under the condition of null hypothesis.Based on these results,we can get the test rejection region.Finally,the Matlab software simulation results show how those procedures work in practice,and applications to real data are also processed.