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The asymptotic theory of linear time-series models

Published online by Cambridge University Press:  14 July 2016

E. J. Hannan
E. J. Hannan*
Affiliation:
The Australian National University
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Abstract

A linear time-series model is considered to be one for which a stationary time series, which is purely non-deterministic, has the best linear predictor equal to the best predictor. A general inferential theory is constructed for such models and various estimation procedures are shown to be equivalent. The treatment is considerably more general than previous treatments. The case where the series has mean which is a linear function of very general kinds of regressor variables is also discussed and a rather general form of central limit theorem for regression is proved. The central limit results depend upon forms of the central limit theorem for martingales.

Keywords

TIME SERIES INFERENCEFOURIER METHODSMARTINGALE CENTRAL LIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 130 - 145
Copyright
Copyright © Applied Probability Trust 1973 

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