A Limit Theorem For Mildly Explosive Autoregression With Stable Errors
AbstractWe 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.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 23 (2007)
Issue (Month): 02 (April)
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- Tassos Magdalinos, 2008. "Mildly explosive autoregression under weak and strong dependence," Discussion Papers 08/05, University of Nottingham, Granger Centre for Time Series Econometrics.
- Zhou, Zhiyong & Lin, Zhengyan, 2014. "Asymptotic theory for LAD estimation of moderate deviations from a unit root," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 25-32.
- Xiaohu Wang & Jun Yu, 2012. "Double Asymptotics for Explosive Continuous Time Models," Working Papers 16-2012, Singapore Management University, School of Economics.
- Magdalinos, Tassos, 2012. "Mildly explosive autoregression under weak and strong dependence," Journal of Econometrics, Elsevier, vol. 169(2), pages 179-187.
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