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ARMA Sieve bootstrap unit root tests

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Author Info

  • Patrick Richard

    ()
    (GREDI, Département d'économique, Université de Sherbrooke)

Abstract

Augmented Dickey-Fuller unit root tests may severely overreject when the DGP is a general linear process. The use of the AR sieve bootstrap, proposed by Park (2002) and Chang and Park (2003), may alleviate this problem. We propose sieve bootstraps based on MA and ARMA approximations. Invariance principles for the partial sum processes built from these sieve bootstrap DGPs are established and a proof of the asymptotic validity of the resulting ADF bootstrap tests is provided. Through Monte Carlo experiments, we find that the rejection probabilities of the MA and ARMA sieve bootstraps are often lower and more robust to the underlying DGP than that of the AR sieve bootstrap. In particular, the new sieve bootstraps perform much better than the AR sieve when a large MA root is present. We also find that the ARMA sieve bootstrap requires only a very parsimonious specification to achieve excellent results.

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File URL: http://gredi.recherche.usherbrooke.ca/wpapers/GREDI-0705.pdf
File Function: First version, 2007
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File URL: http://gredi.recherche.usherbrooke.ca/wpapers/GREDI-0705R.pdf
File Function: Revised version, July 2009
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Bibliographic Info

Paper provided by Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke in its series Cahiers de recherche with number 07-05.

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Length: 38 pages
Date of creation: 2007
Date of revision: Jul 2009
Handle: RePEc:shr:wpaper:07-05

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Related research

Keywords: Sieve bootstrap; Unit root; ADF tests; ARMA approximations; Invariance Principle;

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References

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  1. Abadir, K.M., 1992. "The Limiting Distribution of the T Ratio Under a Unit Root," Papers 1992-2, American Cairo - Economics and Political Sciences.
  2. repec:rus:hseeco:4965 is not listed on IDEAS
  3. Russell Davidson & James Mackinnon, 2006. "Improving the reliability of bootstrap tests with the fast double bootstrap," Working Papers halshs-00439247, HAL.
  4. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(02), pages 469-490, April.
  5. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
  6. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
  7. Donald W.K. Andrews, 2002. "The Block-block Bootstrap: Improved Asymptotic Refinements," Cowles Foundation Discussion Papers 1370, Cowles Foundation for Research in Economics, Yale University.
  8. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, 07.
  9. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
  10. Parker, Cameron & Paparoditis, Efstathios & Politis, Dimitris N., 2006. "Unit root testing via the stationary bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 601-638, August.
  11. repec:cup:etheor:v:11:y:1995:i:4:p:775-93 is not listed on IDEAS
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Citations

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Cited by:
  1. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
  2. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Papers 1127, Queen's University, Department of Economics.
  3. Patrick Marsh, . "Saddlepoint Approximations for Optimal Unit Root Tests," Discussion Papers 09/31, Department of Economics, University of York.
  4. Richard, Patrick, 2009. "Modified fast double sieve bootstraps for ADF tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4490-4499, October.

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