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	Structure of a double autoregressive process driven by a hidden Markov chain
	Liu, Ji-Chun ; Liu JC(刘继春)
	2012-07
关键词	Markov-switching AR-ARCH Strict stationarity Geometric ergodicity Moments
英文摘要	This paper considers a new so-called autoregressive process with ARCH(1) errors driven by a hidden Markov chain, Xt+1 = alpha(Delta(t+1))X-t + eta(t+1) root beta(Delta(t+1)) + lambda(Delta(t+1))X-t(2), t is an element of N, where (eta(t)) is a sequence of independent and identically distributed standard normal random variables, and (Delta(t)) is a Markov chain with finite state space. Some structural properties of this new autoregressive process are considered. A sufficient condition for the existence of the strictly stationary and geometrically ergodic solution of the process is presented. The condition for this is only E [ln vertical bar alpha (Delta(t)) + eta(t) root lambda(Delta(t))vertical bar] < 0. Moreover, some simple conditions for the existence of the moments of the process are also derived. (C) 2012 Elsevier By. All rights reserved.; NSF China [11071202]; NSF Fujian Province of China [2008J0207]
语种	英语
出版者	ELSEVIER SCIENCE BV
内容类型	期刊论文
源URL	[http://dx.doi.org/10.1016/j.spl.2012.04.001]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Liu, Ji-Chun,Liu JC. Structure of a double autoregressive process driven by a hidden Markov chain[J],2012.
APA	Liu, Ji-Chun,&刘继春.(2012).Structure of a double autoregressive process driven by a hidden Markov chain..
MLA	Liu, Ji-Chun,et al."Structure of a double autoregressive process driven by a hidden Markov chain".(2012).

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