The Annals of Statistics

Covariance Matrices Characterization by a Set of Scalar Partial Autocorrelation Coefficients

Hideaki Sakai

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Abstract

It has been shown that the autocovariance matrices of a stationary multivariate time series can be uniquely characterized by a sequence of the normalized partial autocorrelation matrices having singular values less than one. In this note, we show that the same autocovariance matrices can be also uniquely characterized by a set of sequences of scalar partial autocorrelation coefficients whose magnitudes are all less than one.

Article information

Source
Ann. Statist., Volume 11, Number 1 (1983), 337-340.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346085

Digital Object Identifier
doi:10.1214/aos/1176346085

Mathematical Reviews number (MathSciNet)
MR684892

Zentralblatt MATH identifier
0503.62082

JSTOR
links.jstor.org

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

Keywords
Partial autocorrelation coefficients multivariate stationary processes circular lattice filtering

Citation

Sakai, Hideaki. Covariance Matrices Characterization by a Set of Scalar Partial Autocorrelation Coefficients. Ann. Statist. 11 (1983), no. 1, 337--340. doi:10.1214/aos/1176346085. https://projecteuclid.org/euclid.aos/1176346085


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