The Annals of Statistics

Canonical Correlations of Past and Future for Time Series: Bounds and Computation

Nicholas P. Jewell, Peter Bloomfield, and Flavio C. Bartmann

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Abstract

This paper continues an investigation into the canonical correlations and canonical components of the past and future of a stationary Gaussian time series which were introduced in Jewell and Bloomfield (1983). Bounds for the maximum canonical correlation are provided under specified conditions on the spectrum of the series. A computational scheme is described for estimating the canonical correlations and components and the procedure is illustrated on the well-known sunspot number series.

Article information

Source
Ann. Statist., Volume 11, Number 3 (1983), 848-855.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346251

Digital Object Identifier
doi:10.1214/aos/1176346251

Mathematical Reviews number (MathSciNet)
MR707935

Zentralblatt MATH identifier
0524.62096

JSTOR
links.jstor.org

Subjects
Primary: 62M15: Spectral analysis
Secondary: 60G25: Prediction theory [See also 62M20] 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]

Keywords
Time series spectrum prediction canonical correlations ARMA

Citation

Jewell, Nicholas P.; Bloomfield, Peter; Bartmann, Flavio C. Canonical Correlations of Past and Future for Time Series: Bounds and Computation. Ann. Statist. 11 (1983), no. 3, 848--855. doi:10.1214/aos/1176346251. https://projecteuclid.org/euclid.aos/1176346251


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