On the First-Order Autoregressive Process with Infinite Variance

Ngai Hang Chan and Lanh Tat Tran

Econometric Theory, 1989, vol. 5, issue 3, 354-362

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.

Date: 1989
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