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A Limit Theorem For Mildly Explosive Autoregression With Stable Errors

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  • Aue, Alexander
  • Horv th, Lajos
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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 -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 Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 23 (2007)
    Issue (Month): 02 (April)
    Pages: 201-220

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    Handle: RePEc:cup:etheor:v:23:y:2007:i:02:p:201-220_07

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    Cited by:
    1. Magdalinos, Tassos, 2012. "Mildly explosive autoregression under weak and strong dependence," Journal of Econometrics, Elsevier, vol. 169(2), pages 179-187.
    2. Tassos Magdalinos, 2008. "Mildly explosive autoregression under weak and strong dependence," Discussion Papers 08/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    3. Xiaohu Wang & Jun Yu, 2012. "Double Asymptotics for Explosive Continuous Time Models," Working Papers 16-2012, Singapore Management University, School of Economics.
    4. 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.

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