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Vector linear time series models: corrections and extensions

Published online by Cambridge University Press:  01 July 2016

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

Keywords

VECTOR ARMA MODELSIDENTIFICATIONLAWS OF LARGE NUMBERSTOPOLOGY OF ARMA STRUCTURES
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 2 , June 1978 , pp. 360 - 372
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, 27–96.Google Scholar
[2] Dunsmuir, W. and Hannan, E. J. (1976) Vector linear time series models. Adv. Appl. Prob. 8, 339–364.Google Scholar
[3] Forney, D. G. Jr. (1975) Minimal bases of rational vector spaces with applications to multivariable linear systems. SIAM J. Control 13, 493–520.CrossRefGoogle Scholar
[4] Hannan, E. J. (1971) The identification problem for multiple equation systems with moving average errors. Econometrica 39, 751–765.Google Scholar
[5] Hannan, E. J. (1976) The identification and parameterisation of armax and state space forms. Econometrica 44, 713–723.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 Scholar