Statistical Analysis And Empirical Research On The First Order Random Coefficient Integer-valued Autoregressive Models

In recent years,time series data with nonlinear structure have been widely used in finance,medical treatment and social science.Integral valued time series,as a branch of it,is one of the important tools to study the number of people,times and other indicators.At present,the research results of integer valued time series are mostly carried out under fixed environment,but in real life,if the model environment changes randomly,the model disturbance should change accordingly.In addition,there are some data with small value but high volatility in real life,such data is nonstationary,and differential processing method is usually adopted to make the data after differential as stable data,but there may be negative phenomenon.The traditional model cannot solve these two problems,the main content of this thesis is to apply the signed thinning operator and introduce random environment.This thesis firstly introduces the basic theory of random environment and signed thinning operator,and present situation of the previous work is described briefly.Next,the random environment process is extended to the first-order integer valued autoregressive model of stochastic coefficients,and a new model is proposed,namely Rr GINARS(1)model,which can solve the non-stationary data in stochastic environment,the statistical properties of the model,such as moment,conditional moment and correlation coefficient,are calculated.Thirdly,Yule-Walker estimators and conditional maximum likelihood Estimators of model parameters are presented,like Sample expectation,sample variance,and first-order sample covariance,and their strong consistency is proved.Fourthly,numerical simulation is carried out to verify that with the increase of sample size,the mean square error tends to 0 and the estimator gradually converges to the true value.Finally,the applicability of the proposed model to solve practical problems was proved by the real data of epidemic prevention and control.