The Annals of Statistics
- Ann. Statist.
- Volume 11, Number 1 (1983), 337-340.
Covariance Matrices Characterization by a Set of Scalar Partial Autocorrelation Coefficients
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.
Ann. Statist., Volume 11, Number 1 (1983), 337-340.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
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
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