A LIMIT THEOREM FOR MILDLY EXPLOSIVE AUTOREGRESSION WITH STABLE ERRORS

Alexander Aue and Lajos Horv th

Econometric Theory, 2007, vol. 23, issue 02, pages 201-220

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 -stable law, (0,2 . Therein, the autoregressive coefficient = n 1 is assumed to satisfy the condition n 1 such that n( n 1) as n . In contrast to the vast majority of existing literature in the area, no specific form of 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.

Date: 2007

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Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:23:y:2007:i:02:p:201-220_07

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