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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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References

Box, G. E. P. and Jenkins, G. M. (1970) Time Series Analysis. Holden Day, San Francisco.Google Scholar
Chaterji, S. D. (1969) An Lp convergence theorem. Ann. Math. Statist. 40, 1068–1070.Google Scholar
Cox, D. R. (1966) The null distribution of the first serial correlation coefficient. Biometrika 53, 623–626.CrossRefGoogle Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II, 2nd edn. Wiley, New York.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.Google Scholar
Kanter, M. (1976) On quotients of moving average processes with infinite mean. Proc. Amer. Math. Soc. 56, 281–287.Google Scholar
Kanter, M. and Steiger, W. L. (1974) Regression and autoregression with infinite variance. Adv. Appl. Prob. 6, 768–783.Google Scholar
Miller, H. D. (1967) A note on sums of independent random variables with infinite 1st moment. Ann. Math. Statist. 38, 751–758.CrossRefGoogle Scholar