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A discrete model for bootstrap iteration

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  • Russell Davidson

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, CIREQ - Centre interuniversitaire de recherche en économie quantitative)

Abstract

The bootstrap can be validated by considering the sequence of P values obtained by bootstrap iteration, rather than asymptotically. If this sequence converges to a random variable with the uniform U(0,1) distribution, the bootstrap is valid. Here, the model is made discrete and finite, characterised by a three-dimensional array of probabilities. This renders bootstrap iteration to any desired order feasible. A unit-root test for a process driven by a stationary MA(1) process is known to be unreliable when the MA(1) parameter is near −1. Iteration of the bootstrap P value to convergence achieves reliable inference unless the parameter value is very close to −1.

Suggested Citation

  • Russell Davidson, 2017. "A discrete model for bootstrap iteration," Post-Print hal-01658497, HAL.
    • Handle: RePEc:hal:journl:hal-01658497
    DOI: 10.1016/j.jeconom.2017.08.005
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    References listed on IDEAS

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    1. Y.F. Chan, Kenny & M.S. Lee, Stephen, 2001. "An exact iterated bootstrap algorithm for small-sample bias reduction," Computational Statistics & Data Analysis, Elsevier, vol. 36(1), pages 1-13, March.
    2. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    3. Davidson, Russell & MacKinnon, James, 2006. "Improving the Reliability of Bootstrap Tests with the Fast Double Bootstrap," Queen's Economics Department Working Papers 273514, Queen's University - Department of Economics.
    4. Russell Davidson, 2007. "Bootstrapping econometric models (in Russian)," Quantile, Quantile, issue 3, pages 13-36, September.
    5. 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.
    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. MacKinnon, James G., 1995. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Queen's Economics Department Working Papers 273322, Queen's University - Department of Economics.
    8. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-618, Nov.-Dec..
    9. MacKinnon, James G, 1994. "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 167-176, April.
    10. Russell Davidson, 2007. "Bootstrapping Econometric Models," Departmental Working Papers 2007-13, McGill University, Department of Economics.
    11. MacKinnon, James G., 1992. "Approximate Asymptotic Distribution Functions for Unit Roots and Cointegration Tests," Queen's Economics Department Working Papers 273255, Queen's University - Department of Economics.
    12. Stephen M. S. Lee, 2003. "Prepivoting by weighted bootstrap iteration," Biometrika, Biometrika Trust, vol. 90(2), pages 393-410, June.
    13. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 95(2), pages 375-389, April.
    14. Russell Davidson, 2010. "Size Distortion of Bootstrap Tests: an Example from Unit Root Testing," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 2(2), pages 169-193, June.
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    Cited by:

    1. Russell Davidson, 2015. "Computing, the bootstrap and economics," Canadian Journal of Economics, Canadian Economics Association, vol. 48(4), pages 1195-1214, November.

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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