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April, 1967 On the Cross Periodogram of a Stationary Gaussian Vector Process
T. Subba Rao
Ann. Math. Statist. 38(2): 593-597 (April, 1967). DOI: 10.1214/aoms/1177698976

Abstract

Bartlett [1] obtained an asymptotic relation connecting the periodogram of a linear process and the periodogram of the residuals with uniform spectrum in the case of one dimensional stationary time series, and using this relation he studied the asymptotic properties of the periodogram. In this paper we obtain some asymptotic relations between the co-periodogram and quadrature periodogram of the residuals in the case of a stationary Gaussian vector process. The covariances of the co-periodogram and quadrature periodogram have also been obtained. Two inequalities connecting the variance and the bandwidth of the cross spectral estimate have been derived.

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T. Subba Rao. "On the Cross Periodogram of a Stationary Gaussian Vector Process." Ann. Math. Statist. 38 (2) 593 - 597, April, 1967. https://doi.org/10.1214/aoms/1177698976

Information

Published: April, 1967
First available in Project Euclid: 27 April 2007

zbMATH: 0166.14503
MathSciNet: MR210273
Digital Object Identifier: 10.1214/aoms/1177698976

Rights: Copyright © 1967 Institute of Mathematical Statistics

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Vol.38 • No. 2 • April, 1967
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