The Annals of Mathematical Statistics

On the Cross Periodogram of a Stationary Gaussian Vector Process

T. Subba Rao

Full-text: Open access

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.

Article information

Source
Ann. Math. Statist., Volume 38, Number 2 (1967), 593-597.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177698976

Digital Object Identifier
doi:10.1214/aoms/1177698976

Mathematical Reviews number (MathSciNet)
MR210273

Zentralblatt MATH identifier
0166.14503

JSTOR
links.jstor.org

Citation

Rao, T. Subba. On the Cross Periodogram of a Stationary Gaussian Vector Process. Ann. Math. Statist. 38 (1967), no. 2, 593--597. doi:10.1214/aoms/1177698976. https://projecteuclid.org/euclid.aoms/1177698976


Export citation