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May, 1978 Covariance Characterization by Partial Autocorrelation Matrices
M. Morf, A. Vieira, T. Kailath
Ann. Statist. 6(3): 643-648 (May, 1978). DOI: 10.1214/aos/1176344208

Abstract

It is known that the autocorrelation function of a stationary discrete-time scalar process can be uniquely characterized by the so-called partial autocorrelation function, which is a sequence of numbers less or equal to one in magnitude. We show here that the matrix covariance function of a multivariate stationary process can be characterized by a sequence of matrix partial correlations, having singular values less than or equal to one in magnitude. This characterization can be used to extend to the multivariate case the so-called maximum entropy spectral analysis method.

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M. Morf. A. Vieira. T. Kailath. "Covariance Characterization by Partial Autocorrelation Matrices." Ann. Statist. 6 (3) 643 - 648, May, 1978. https://doi.org/10.1214/aos/1176344208

Information

Published: May, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0413.62072
MathSciNet: MR478519
Digital Object Identifier: 10.1214/aos/1176344208

Subjects:
Primary: 62M10
Secondary: 60G10 , 62M15 , 62N15

Keywords: multivariate maximum entropy method of spectral analysis , multivariate stationary processes , Partial autocorrelation matrices

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 3 • May, 1978
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