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

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  • Horváth, Lajos
  • Kokoszka, Piotr

Abstract

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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Bibliographic Info

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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Related research

Keywords: Bootstrap Heavy tails Stable distribution Unit root;

References

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  1. 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.
  2. Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, September.
  3. 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.
  4. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-69, December.
  5. 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.
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Cited by:
  1. Qin, Ruibing & Tian, Zheng & Jin, Hao & Zhang, Xiaowei, 2010. "Strong convergence rate of robust estimator of change point," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2026-2032.
  2. Jin, Hao & Tian, Zheng & Qin, Ruibing, 2009. "Bootstrap tests for structural change with infinite variance observations," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 1985-1995, October.
  3. Kirman, Alan & Teyssiere, Gilles, 2005. "Testing for bubbles and change-points," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 765-799, April.
  4. Chen, Zhanshou & Jin, Zi & Tian, Zheng & Qi, Peiyan, 2012. "Bootstrap testing multiple changes in persistence for a heavy-tailed sequence," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2303-2316.
  5. Jin, Hao & Zhang, Jinsuo, 2011. "Modified tests for variance changes in autoregressive regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1099-1109.

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