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On the First-Order Autoregressive Process with Infinite Variance

Published online by Cambridge University Press:  18 October 2010

Ngai Hang Chan  and
Lanh Tat Tran
Ngai Hang Chan
Affiliation:
Indiana University
Lanh Tat Tran
Affiliation:
Indiana University
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Abstract

For a first-order autoregressive process Yt = βYt−1 + ∈t where the ∈t'S are i.i.d. and belong to the domain of attraction of a stable law, the strong consistency of the ordinary least-squares estimator bn of β is obtained for β = 1, and the limiting distribution of bn is established as a functional of a Lévy process. Generalizations to seasonal difference models are also considered. These results are useful in testing for the presence of unit roots when the ∈t'S are heavy-tailed.

Type
Articles
Information
Econometric Theory , Volume 5 , Issue 3 , December 1989 , pp. 354 - 362
Copyright
Copyright © Cambridge University Press 1989

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