Estimation For Some Integer-valued Autoregressive Models Under Random Environment

The integer-valued time series,as one of the important branch of time series,is widely used in the biology,medicine,crime,finance,psychology,environmental science.With the further research of the integer-valued time series,researchers have found that integer-valued time series data from real life will be affected by an environmental mutation.In order to solve the problem of the impact of environmental changes,this thesis considers introducing random environments into three types of the integer-valued autoregressive model,and obtains the integer-valued autoregressive model under random environments.At the same time,the numerical characteristics of proposed models are studied,and the expressions of every-order moment are obtained.This thesis establishes Yule-Walker estimators of model parameters,and discusses the strong consistency of the obtained estimators.Finally,a simulation is carried out to verify the feasibility of parameter estimation.This ideal breaks through the limitation of traditional integer-valued autoregressive models,makes the proposed model can adapt to the sudden environment change,and gives new research thinking to the integer-valued autoregressive model.The contents of this thesis are as follows.In Chapter 1,we introduce the research status in quo about the integer-valued time series.In Chapter 2,this thesis introduces the definition about the negative binomial thinning.The threshold integer-valued autoregressive model under random environment is introduced.This chapter studies definition and numerical characteristics of the proposed model,discusses the estimation problem of the proposed model parameters and proves the strong consistency of Yule-Walker estimators.In Chapter 3,we propose the random coefficient integer-valued autoregressive model under random environment,give the definition and establish Yule-Walker estimators of parameters.The strong consistency of the estimator is discussed.The estimation effect is studied through numerical simulation.The simulation studies demonstrate that the Yule-Walker method can be used for statistical inference of the proposed model.In Chapter 4,the model presented in Chapter 3 is extended to the high-order model.The numerical characteristics and parameters estimation of the proposed model are discussed.In Chapter 5,we summarize and forecast about this thesis.