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A bootstrap approximation to a unit root test statistic for heavy-tailed observations

  • Horváth, Lajos
  • Kokoszka, Piotr

In the context of the AR(1) model with innovations in the domain of attraction of an [alpha]-stable law, we develop a residual bootstrap approximation to the distribution of a least-squares estimator of the autoregressive parameter when this parameter is equal to unity. Our procedure requires drawing bootstrap samples of size m [infinity] and m/n-->0. An analogous result is established for the partial sum process of the bootstrap noise sequence.

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Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 62 (2003)
Issue (Month): 2 (April)
Pages: 163-173

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Handle: RePEc:eee:stapro:v:62:y:2003:i:2:p:163-173
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  1. Chan, Ngai Hang & Tran, Lanh Tat, 1989. "On the First-Order Autoregressive Process with Infinite Variance," Econometric Theory, Cambridge University Press, vol. 5(03), pages 354-362, December.
  2. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
  3. Wang, Qiying & Lin, Yan-Xia & Gulati, Chandra M., 2003. "Asymptotics For General Fractionally Integrated Processes With Applications To Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(01), pages 143-164, February.
  4. Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, September.
  5. Ling, Shiqing & Li, W.K., 2003. "Asymptotic Inference For Unit Root Processes With Garch(1,1) Errors," Econometric Theory, Cambridge University Press, vol. 19(04), pages 541-564, August.
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