Matrix polynomials orthogonal on the unit circle and accuracy of autoregressive models
type: Item
instance of: scholarly article
title: Matrix polynomials orthogonal on the unit circle and accuracy of autoregressive models
zbMATH Open document ID: 0862.65098
DOI: 10.1016/0377-0427(95)00130-0
author: M.-P. Mignolet
published in: Journal of Computational and Applied Mathematics
publication date: 1997-05-25T00:00:00Z
review text: Orthogonal matrix polynomials on the unit circle with respect to a positive definite matrix valued measure \(K(\theta)d\theta\) are studied. An upper bound for the accuracy of autoregressive modeling of discrete stationary vector random processes of the spectral matrix \(K(\theta)\) is given in terms of \(K(\theta)\). This permits an a priori estimation of the order of the autoregressive model. A simple relationship is derived that relates some Fourier coefficients of the target spectral matrix and its autoregressive counterpart. The results of the paper extend previously known results for the scalar orthogonal polynomials [see the author and \textit{P. D. Spanos}, Int. J. Non-Linear Mech. 26, No. 6, 911-930 (1991; Zbl 0825.65130)] to the matrix case.
reviewed by: Leiba Rodman
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 903475
zbMATH Keywords: orthogonal matrix polynomials
zbMATH Keywords: autoregressive modeling
zbMATH Keywords: discrete stationary vector random processes
zbMATH Keywords: spectral matrix
zbMATH Keywords: Fourier coefficients
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00130-0
OpenAlex ID: W1982035773
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description: scientific article; zbMATH DE number 903475