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.
Publié le : 1978-05-14
Classification:
Partial autocorrelation matrices,
multivariate stationary processes,
multivariate maximum entropy method of spectral analysis,
62M10,
62N15,
62M15,
60G10
@article{1176344208,
author = {Morf, M. and Vieira, A. and Kailath, T.},
title = {Covariance Characterization by Partial Autocorrelation Matrices},
journal = {Ann. Statist.},
volume = {6},
number = {1},
year = {1978},
pages = { 643-648},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344208}
}
Morf, M.; Vieira, A.; Kailath, T. Covariance Characterization by Partial Autocorrelation Matrices. Ann. Statist., Tome 6 (1978) no. 1, pp. 643-648. http://gdmltest.u-ga.fr/item/1176344208/