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Vector linear time series models: corrections and extensions

Published online by Cambridge University Press:  01 July 2016

M. Deistler
Affiliation:
University of Bonn
W. Dunsmuir
Affiliation:
The Australian National University
E. J. Hannan
Affiliation:
The Australian National University

Abstract

In this paper some theorems of Dunsmuir and Hannan [2] are corrected. The topological structure of spaces of (likelihood) equivalence classes of arma structures is more closely investigated and its relation to the statistical problem is elucidated. The formulation is also made more general.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1978 

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References

[1] Akaike, H. (1976) Canonical correlation analysis of time series and the use of the information criterion. In System Identification: Advances and Case Studies, ed. Mehra, R. K. and Lainiotis, D. G. Academic Press, New York, 2796.CrossRefGoogle Scholar
[2] Dunsmuir, W. and Hannan, E. J. (1976) Vector linear time series models. Adv. Appl. Prob. 8, 339364.CrossRefGoogle Scholar
[3] Forney, D. G. Jr. (1975) Minimal bases of rational vector spaces with applications to multivariable linear systems. SIAM J. Control 13, 493520.CrossRefGoogle Scholar
[4] Hannan, E. J. (1971) The identification problem for multiple equation systems with moving average errors. Econometrica 39, 751765.CrossRefGoogle Scholar
[5] Hannan, E. J. (1976) The identification and parameterisation of armax and state space forms. Econometrica 44, 713723.CrossRefGoogle Scholar
[6] Heymann, M. (1975) Structure and Realization Problems in the Theory of Dynamical Systems. Springer-Verlag, New York.Google Scholar
[7] Ward, L. E. (1972) Topology. Dekker, New York.Google ScholarPubMed
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