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

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Abstract

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.

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Correspondence to Zhenting Hou.

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Manuscript received: January 2004/Final version received: July 2004

This work was partially supported by NSFC of China (No.10171009)

Research Fund for Ph.D Programs of MOE of China (No.20010533001).

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Hou, Z., Yu, Z. & Shi, P. Study on a class of nonlinear time series models and ergodicity in random environment domain. Math Meth Oper Res 61, 299–310 (2005). https://doi.org/10.1007/s001860400399

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  • DOI: https://doi.org/10.1007/s001860400399

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