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ARMA Sieve bootstrap unit root tests

Author

Listed:
  • 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.

Suggested Citation

  • Patrick Richard, 2007. "ARMA Sieve bootstrap unit root tests," Cahiers de recherche 07-05, Departement d'économique de l'École de gestion à l'Université de Sherbrooke, revised Jul 2009.
    • Handle: RePEc:shr:wpaper:07-05
    as

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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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    References listed on IDEAS

    as
    1. Anders Rygh Swensen, 2003. "Bootstrapping unit root tests for integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 99-126, January.
    2. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    3. 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, July.
    4. Donald W. K. Andrews, 2004. "the Block-Block Bootstrap: Improved Asymptotic Refinements," Econometrica, Econometric Society, vol. 72(3), pages 673-700, May.
    5. Abadir, Karim M., 1995. "The Limiting Distribution of the t Ratio Under a Unit Root," Econometric Theory, Cambridge University Press, vol. 11(4), pages 775-793, August.
    6. Davidson, Russell & MacKinnon, James G., 2007. "Improving the reliability of bootstrap tests with the fast double bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3259-3281, April.
    7. repec:cup:etheor:v:11:y:1995:i:4:p:775-93 is not listed on IDEAS
    8. 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.
    9. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    10. 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.
    11. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(2), pages 469-490, April.
    12. Abadir, K.M., 1992. "The Limiting Distribution of the T Ratio Under a Unit Root," Papers 1992-2, American Cairo - Economics and Political Sciences.
    13. repec:rus:hseeco:4965 is not listed on IDEAS
    14. 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.
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    Cited by:

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

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    More about this item

    Keywords

    Sieve bootstrap; Unit root; ADF tests; ARMA approximations; Invariance Principle;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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