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A Limit Theorem For Mildly Explosive Autoregression With Stable Errors


  • Aue, Alexander
  • Horváth, Lajos


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 Ï = Ï n > 1 is assumed to satisfy the condition Ï n → 1 such that n(Ï n − 1) → ∞ as n → ∞. In contrast to the vast majority of existing literature in the area, no specific form of Ï 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.

Suggested Citation

  • Aue, Alexander & Horváth, Lajos, 2007. "A Limit Theorem For Mildly Explosive Autoregression With Stable Errors," Econometric Theory, Cambridge University Press, vol. 23(2), pages 201-220, April.
  • Handle: RePEc:cup:etheor:v:23:y:2007:i:02:p:201-220_07

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    Cited by:

    1. 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.
    2. Wang, Xiaohu & Yu, Jun, 2016. "Double asymptotics for explosive continuous time models," Journal of Econometrics, Elsevier, vol. 193(1), pages 35-53.
    3. Tassos Magdalinos, 2008. "Mildly explosive autoregression under weak and strong dependence," Discussion Papers 08/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    4. Stelios Arvanitis & Tassos Magdalinos, 2018. "Mildly Explosive Autoregression Under Stationary Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 892-908, November.
    5. 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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