Garch Model With Random Delay Strict Stationary And Ergodicity,

In recent several decades,the development of time series analysis is rapid.Especially the investigation of linear time series,the systematic and abundant achievements have been obtained.However,the statisticians and econmetricians have gradually paid attention to the investigation of nonlinear time series for the last two decades.In the last decade,there exist two active lines on the investigation of nonlinear time series.One is the autoregressive conditional heteroscedas-ticity(ARCH) model,the another is the nonstationary time series model. The concept of ARCH, which stands for autoregressive heteroscedasticity was first introduced by Engle(1982) to handle time series with a changing conditional variance.Bollerslev(1986) extended the ARCH model into the so-called generalized ARCH(GARCH) model.This class of models has important applications,particularly in finance and economics (see,eg.,Bo-llerslev,Engle and Woodridge(1988),Bollerslev,Chou and Kroner(1992)).According to the documents about the time series model in the past, whether it was in the linear time series model or not, its disturbances had been supposed to be a single white noise series and there was a specially fixed delay constant in every model. There is an obvious limitation in it, in other words, it can't describe the fact that the system's disturbance or the delay in it change stochastically because of affection of various random factors. Professor Hou Zhengting of the Institute of Probability & Statistics (IPS), the Central South University, has brought forward the Random Environment Time Series Model (RETSM) firstly to try to resolve the problem that the disturbance would be affected by random factors, and have carried out a lot of researches and attained a series achievement. To resolve the problem that the delay would be affected by random factors, basing on Hou Zhenting's theory, my mentor put forward a time series model that its delay controlled by a Markov chain with finite states, as a generalization of the time series model.In this thesis, following the idea and method ahead, applying the Markovnization and the theories of general state space Markov Chain, I have studied some time series models with stochastic delay, and have deduced some sufficient conditions about the companion geometric ergodicity of these models.Four parts compose this thesis as following:Chapter 1 introduces the research status in quo about the time series models.Chapter 2, a basic knowledge of this thesis, briefly presents some basic notions of the general states Markov chain and the ergodicity of the Markov chain.In chapter 3,I first study the GARCH model with a stochastic delay and get corresponding Markov chain theory, and give the definition of companion ergodicity and companion geometric ergodicity of this model. Second, I get a sufficient condition of the companion strict stationary ergodicity of this model by applying the theories constructed formerly.Chapter 4 researches of the strict stationary ergodicity of a nonlinear time series model by applying the same method used in chapter 3.At last, I get a sufficient condition of the strict stationary ergodicity to the general nonlinear time series model.