Study on a class of nonlinear time series models and ergodicity in random environment domain

In this paper, we study the problem of a variety of nonlinear threshold autoregressive model X n +1 =ϕ(X n )+ɛ n +1 (Z n +1 ) in which {Z n } is a Markov chain with finite state space, and for every state i of the Markov chain, {ɛ n (i)} is a sequence of independent and identically distributed random variables. Also, the limit behavior of the sequence {X n } defined by the above model is investigated. Some new novel results on the underlying models are presented. Copyright Springer-Verlag 2005