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