Structure of a double autoregressive process driven by a hidden Markov chain
- 数学科学－已发表论文 
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.
CitationSTATISTICS & PROBABILITY LETTERS，2012,82（7）：1468-1473