On the First-Order Autoregressive Process with Infinite Variance
- 1 December 1989
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 5 (3) , 354-362
- https://doi.org/10.1017/s0266466600012561
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.Keywords
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