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June, 1988 Unit Canonical Correlations between Future and Past
E. J. Hannan, D. S. Poskitt
Ann. Statist. 16(2): 784-790 (June, 1988). DOI: 10.1214/aos/1176350836


Stationary vector ARMA processes $x(t), t = 0, \pm 1, \pm 2, \cdots$, of $n$ components are considered that are of full rank, and the situation where there are linear functions of the future $x(t), t > 0$, and the past $x(t), t \leq 0$ (more properly the present and the past) that have unit correlation. It is shown that the number of linearly independent such pairs (i.e., the number of unit canonical correlations between future and past) is the number of zeros of the determinant of the transfer functions, from innovations to outputs, that lie on the unit circle, counting these with their multiplicities.


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E. J. Hannan. D. S. Poskitt. "Unit Canonical Correlations between Future and Past." Ann. Statist. 16 (2) 784 - 790, June, 1988.


Published: June, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0646.62082
MathSciNet: MR947578
Digital Object Identifier: 10.1214/aos/1176350836

Primary: 60G10
Secondary: 60G35, 62M20

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 2 • June, 1988
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