On the First-Order Autoregressive Process with Infinite Variance

For a first-order autoregressive process Y = β Y t−1 + null where the null null '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 b of β is obtained for β = 1, and the limiting distribution of b is established as a functional of a Levy process. Generalizations to seasonal difference models are also considered. These results are useful in testing for the presence of unit roots when the null null 'S are heavy-tailed.

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