Notes on poles of autoregressive type model, I: Non-robust singular pole
type: Item
instance of: scholarly article
title: Notes on poles of autoregressive type model, I: Non-robust singular pole
zbMATH Open document ID: 0641.62053
DOI: 10.1016/0022-247X(87)90027-8
author: Kuniharu Kishida
author: Sumasu Yamada
author: Keisuke Bekki
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: Let \(x(t)=[x_ 1(t),x_ 2(t),x_ 3(t)]'\) be a 3-dimensional AR(1) process. Assume that only \(x_ 1(t)\) is observable. Then \(x_ 1(t)\) is described by an ARMA (3,2) model, which can be written in an AR(\(\infty)\) form. If only a finite number of members of this AR(\(\infty)\) expression is considered, we get a truncated AR(TAR) model. Using Rouché's theorem, the authors investigate location of poles of the TAR model and their relations to the poles of the original ARMA(3,2) model. It is also shown that the zero of the ARMA(3,2) model closest to the unit circle has an important role in the convergence of spectral density functions of the TAR models to that of the ARMA(3,2) model.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 93E12
zbMATH DE Number: 4044979
zbMATH Keywords: non-robust singular pole
zbMATH Keywords: autoregressive type approximation
zbMATH Keywords: zero closest to unit circle
zbMATH Keywords: truncated AR processes
zbMATH Keywords: ARMA (3,2) model
zbMATH Keywords: Rouché's theorem
zbMATH Keywords: location of poles
zbMATH Keywords: TAR model
zbMATH Keywords: convergence of spectral density functions
reviewed by: Jiří Anděl
MaRDI profile type: Publication
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full work available at URL: 0022-247x(87)90027-8
OpenAlex ID: W4235718433
description: scientific article; zbMATH DE number 4044979