The Annals of Statistics

Covariance Characterization by Partial Autocorrelation Matrices

M. Morf, A. Vieira, and T. Kailath

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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.

Article information

Ann. Statist., Volume 6, Number 3 (1978), 643-648.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62N15 62M15: Spectral analysis 60G10: Stationary processes

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


Morf, M.; Vieira, A.; Kailath, T. Covariance Characterization by Partial Autocorrelation Matrices. Ann. Statist. 6 (1978), no. 3, 643--648. doi:10.1214/aos/1176344208.

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