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On the First-Order Autoregressive Process with Infinite Variance

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  • Chan, Ngai Hang
  • Tran, Lanh Tat

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.

Suggested Citation

  • Chan, Ngai Hang & Tran, Lanh Tat, 1989. "On the First-Order Autoregressive Process with Infinite Variance," Econometric Theory, Cambridge University Press, vol. 5(3), pages 354-362, December.
    • Handle: RePEc:cup:etheor:v:5:y:1989:i:03:p:354-362_01
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