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Autoregressive processes with infinite variance

Published online by Cambridge University Press:  14 July 2016

E. J. Hannan  and
Marek Kanter
E. J. Hannan
Affiliation:
The Australian National University
Marek Kanter
Affiliation:
University of New South Wales
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Abstract

The least squares estimators βi(N), j = 1, …, p, from N data points, of the autoregressive constants for a stationary autoregressive model are considered when the disturbances have a distribution attracted to a stable law of index α < 2. It is shown that N1/δ(βi(N) – β) converges almost surely to zero for any δ > α. Some comments are made on alternative definitions of the βi(N).

Keywords

AUTOREGRESSIONSTABLE LAWSSTRONG LAWLEAST SQUARESYULE-WALKER RELATIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 411 - 415
Copyright
Copyright © Applied Probability Trust 1977 

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