Verifying irreducibility and continuity of a nonlinear time series
type: Item
instance of: scholarly article
title: Verifying irreducibility and continuity of a nonlinear time series
zbMATH Open document ID: 0938.62090
DOI: 10.1016/S0167-7152(98)00081-9
author: Daren B. H. Cline
author: Huay-min H. Pu
published in: Statistics \& Probability Letters
publication date: 2000-06-04T00:00:00Z
review text: Let \(\{e_t\}\) be i.i.d. random vectors. Define an \(m\)-dimensional nonlinear autoregressive time series \(\xi_t = \zeta(e_t;\xi_{t-1},\dots,\xi_{t-p})\), \(t\geq 1\), where \(\zeta\) is a Borel measurable mapping. Then \(\{\xi_t\}\) is embedded in a Markov chain \(\{X_t\}\) with \(X_t=(\xi_t,\dots,\xi_{t-p+1})\). The authors present conditions under which the chain is irreducible, or aperiodic, or has smooth transitions. These properties can be used for establishing stability of time series. It is shown that conditionally heteroscedastic (ARCH) processes, bilinear processes, SETAR processes, and mixture transition distribution processes are special cases of the general model investigated in this paper.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 1346154
zbMATH Keywords: aperiodicity
zbMATH Keywords: T-chains
zbMATH Keywords: Feller chains
zbMATH Keywords: psi-irreducibility
zbMATH Keywords: nonlinear time series models
reviewed by: Jiří Anděl
MaRDI profile type: Publication
cites work: Q4606219
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description: scientific article; zbMATH DE number 1346154