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Spectral characterization of the Wold–Zasuhin decomposition and prediction-error operator

Published online by Cambridge University Press:  24 October 2008

S. C. Power
S. C. Power
Affiliation:
Department of Mathematics, University of Lancaster, Lancaster LA 1 4YF
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Extract

Over thirty years ago Wiener and Masani pointed out in the introduction of their celebrated paper [31] that for a general multivariate stationary stochastic process no relation had been given for the prediction-error matrix in terms of the spectrum of the process. In particular it was unknown how to characterize the rank of the process in spectral terms (cf. Masani[12], p. 369, question 1). Despite explicit progress in this connection with certain regular processes, such as the series representations in [11, 19, 22, 32], or the iterative approach of [28, 29], and despite progress in the structure theory of degenerate processes ([8, 10, 14, 15, 26]), a general relation or series expression has remained elusive.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 3 , November 1991 , pp. 559 - 567
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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