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Vector linear time series models

Published online by Cambridge University Press:  01 July 2016

W. Dunsmuir  and
E. J. Hannan
W. Dunsmuir
Affiliation:
Australian National University
E. J. Hannan
Affiliation:
Australian National University
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Abstract

This paper presents proofs of the strong law of large numbers and the central limit theorem for estimators of the parameters in quite general finite-parameter linear models for vector time series. The estimators are derived from a Gaussian likelihood (although Gaussianity is not assumed) and certain spectral approximations to this. An important example of finite-parameter models for multiple time series is the class of autoregressive moving-average (ARMA) models and a general treatment is given for this case. This includes a discussion of the problems associated with identification in such models.

Keywords

LINEAR PROCESSESVECTOR ARMA MODELSIDENTIFICATIONLIMIT THEOREMSMARTINGALESFOURIER METHODS
Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 2 , June 1976 , pp. 339 - 364
Copyright
Copyright © Applied Probability Trust 1976 

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