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Spectral factorisation and prediction of multivariate processes with time-dependent rational spectral density matrices

Published online by Cambridge University Press:  17 February 2009

N. M. Spencer  and
V. V. Anh
N. M. Spencer
Affiliation:
School of Mathematics, Queensland Institute of Technology, Brisbane Q 4001, Australia.
V. V. Anh
Affiliation:
School of Mathematics, Queensland Institute of Technology, Brisbane Q 4001, Australia.
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Abstract

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This paper considers discrete multivariate processes with time-dependent rational spectral density matrices and gives a solution to the spectral factorisation problem. As a result, the corresponding state space representation for the process is obtained. The relationship between multivariate processes with time-dependent rational spectral density matrix functions and multivariate ARMA processes with time-dependent coefficients is discussed. Solutions for the prediction problem are given for the case when only finite data is available and the case when the whole history of the process is known.

Type
Research Article
Information
The ANZIAM Journal , Volume 33 , Issue 2 , October 1991 , pp. 192 - 210
Copyright
Copyright © Australian Mathematical Society 1991

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