On probabilistic properties of nonlinear \(\text{ARMA}(p,q)\) models
type: Item
instance of: scholarly article
title: On probabilistic properties of nonlinear \(\text{ARMA}(p,q)\) models
zbMATH Open document ID: 0986.60033
DOI: 10.1016/S0167-7152(99)00096-6
author: Oesook Lee
published in: Statistics \& Probability Letters
publication date: 2002-02-03T00:00:00Z
review text: The nonlinear ARMA model \(X_{n+1}=h(e_{n-q+1},\dots,e_n, X_{n-p+1},\dots,X_n)+e_{n+1}\) is considered where \(h\) is a measurable function and \(\{e_t\}\) is a sequence of i.i.d. random variables with \(E|e_n|<\infty\) such that \(e_n\) is independent of \(X_{n-1},\dots,X_0\). Sufficient conditions for stationarity and geometric ergodicity of \(\{X_n\}\) are derived using properties of the associated Markov chain. Technically, the method is based on an approximation of \(h({\mathbf x})\) by \(\sum_{i=1}^q \psi_i({\mathbf x})z_i+\sum_{i=1}^p \varphi_i({\mathbf x})x_i\) where \({\mathbf x}=(z_1,\dots,z_q,x_1,\dots, x_p)\).
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 1422608
zbMATH Keywords: nonlinear ARMA(p,q) model
zbMATH Keywords: Markov chain
zbMATH Keywords: stationarity
zbMATH Keywords: ergodicity
zbMATH Keywords: geometric ergodicity
reviewed by: Jiří Anděl
MaRDI profile type: Publication
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full work available at URL: s0167-7152(99)00096-6
OpenAlex ID: W2071367031
description: scientific article; zbMATH DE number 1422608