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A LIMIT THEOREM FOR MILDLY EXPLOSIVE AUTOREGRESSION WITH STABLE ERRORS

Published online by Cambridge University Press:  30 January 2007

Alexander Aue  and
Lajos Horváth
Alexander Aue
Affiliation:
Clemson University
Lajos Horváth
Affiliation:
University of Utah
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Abstract

We discuss the limiting behavior of the serial correlation coefficient in mildly explosive autoregression, where the error sequence is in the domain of attraction of an α-stable law, α ∈ (0,2]. Therein, the autoregressive coefficient ρ = ρn > 1 is assumed to satisfy the condition ρn → 1 such that n(ρn − 1) → ∞ as n → ∞. In contrast to the vast majority of existing literature in the area, no specific form of ρ is required. We show that the serial correlation coefficient converges in distribution to a ratio of two independent stable random variables.The authors thank P.C.B. Phillips and two anonymous referees for a very careful reading of the manuscript, pointing out several mistakes, and providing shorter and simpler proofs. This research was partially supported by NATO grant PST.EAP.CLG 980599 and NSF-OTKA grant INT-0223262. This work was done while the first author was at the University of Utah.

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 2 , April 2007 , pp. 201 - 220
Copyright
© 2007 Cambridge University Press

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