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Covariance Characterization by Partial Autocorrelation Matrices

M. Morf, A. Vieira and T. Kailath
The Annals of Statistics
Vol. 6, No. 3 (May, 1978), pp. 643-648
Stable URL: http://www.jstor.org/stable/2958567
Page Count: 6
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Covariance Characterization by Partial Autocorrelation Matrices
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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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