Time Series With Random Delay Anaysis

The main part of this dissertation consists of five chapters:In the first chapter, some necessary preliminaries which belong toergodic theory of Markov chain on general state space are introducedbriefly.Form the second to the fifith chapter, the limit behacior of thefollowing each class of nonlinear time series models is investigated inture:1,Nonlinear autoregressive model with a random delay X(n+1)=f_Zn+1(X(n), X(n-1),..., X(n-Z_n+1))+ε_n+12,Nonlinear autoregressive model with a random environment and witha random delay X(n+1)=f₍Z_n+1(X(n), X(n-1),..., X(n-Z_n+1))+ε_n+1(Z_n+1)3,Stochastic conditional variance nonlinear autoregressive model with arandom delayX(n+1)=f_Zn+1(X(n),X(n-1),...,X(n-Z_n+1))+H₍Z_n+1(X(n),X(n-1),...,X(n-Z_n+1))ε_n+1and its two classes of extended forms.Two classes of time series models with countably many ofinterference terms and a random delay4,X(n+1)=f₍Z_n+1(X(n),X(n-1),...,X(n-Z_n+1))+ε_n+1(W_n+1)and 5,X(n+1)=f_Zn+1(X(n),..., X(n-Z_n+1))+H_Zn+1(X(n),..., X(n-Z_n+1))ε_n+1(W_n+1)The time series models which have common form6,X(n+1)=T_Zn+1(X(n),X(n-1),...,X(n-Z_n+1);ε_n+1(Z_n+1))Gernerally speaking, the sequence {X(n)} determined by the aboveeach class of time series models is not a Markov chains. In order tostudy such models, we introduce the concepts of adjoint ergodicity andadjoint geometrical ergodicity to describe their limit property, dig thepotential of the research methods applied in studying the ergodicity ofnonlinear time series during the recent 20 years. We generalize theLyapunov function approach, which was used in studying the stability ofdeterminate dynamical system and in studying the ergodicity of Markovchains on general state space, to study the adjoint ergodicity ofnon-Markov time series mentioned above. The correspondingsufficaiency criterion is established.