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Improving the Reliability of Bootstrap Tests with the Fast Double Bootstrap

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Author Info

  • Russell Davidson

    ()
    (McGill University)

  • James G. MacKinnon

    ()
    (Queen's University)

Abstract

We first propose two procedures for estimating the rejection probabilities of bootstrap tests in Monte Carlo experiments without actually computing a bootstrap test for each replication. These procedures are only about twice as expensive (per replication) as estimating rejection probabilities for asymptotic tests. We then propose a new procedure for computing bootstrap P values that will often be more accurate than ordinary ones. This "fast double bootstrap" is closely related to the double bootstrap, but it is far less computationally demanding. Simulation results for three different cases suggest that this procedure can be very useful in practice.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1044.pdf
File Function: First version 2006
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1044.

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Length: 34 pages
Date of creation: Mar 2006
Date of revision:
Publication status: forthcoming in Computational Statistics and Data Analysis
Handle: RePEc:qed:wpaper:1044

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Keywords: bootstrap test; double bootstrap; Monte Carlo experiment; rejection frequency; fast double bootstrap; FDB;

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References

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  1. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
  2. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
  3. Omtzigt Pieter & Fachin Stefano, 2002. "Bootstrapping and Bartlett corrections in the cointegrated VAR model," Economics and Quantitative Methods qf0212, Department of Economics, University of Insubria.
  4. Jean-FranÁois Lamarche, 2004. "The Numerical Performance of Fast Bootstrap Procedures," Computational Economics, Society for Computational Economics, vol. 23(4), pages 379-389, 06.
  5. Russell Davidson & James G. MacKinnon, 2004. "The Power of Bootstrap and Asymptotic Tests," Working Papers 1035, Queen's University, Department of Economics.
  6. Dufour, Jean-Marie & Khalaf, Lynda & Bernard, Jean-Thomas & Genest, Ian, 2004. "Simulation-based finite-sample tests for heteroskedasticity and ARCH effects," Journal of Econometrics, Elsevier, vol. 122(2), pages 317-347, October.
  7. Davidson, R. & Mackinnon, J.G., 1997. "Bootstrap Tests of Nonnested Linear Regression Models," ASSET - Instituto De Economia Publica 170, ASSET (Association of Southern European Economic Theorists).
  8. Park, Joon, 2002. "Bootstrap Unit Root Tests," Working Papers 2003-04, Rice University, Department of Economics.
  9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  10. Davidson, Russell & MacKinnon, James G, 1999. "Bootstrap Testing in Nonlinear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 487-508, May.
  11. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
  12. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-21, May.
  13. Davidson, Russell & MacKinnon, James G., 1984. "Convenient specification tests for logit and probit models," Journal of Econometrics, Elsevier, vol. 25(3), pages 241-262, July.
  14. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
  15. Russell Davidson & James MacKinnon, 2002. "Fast Double Bootstrap Tests Of Nonnested Linear Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 419-429.
  16. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
  17. Russell Davidson & James G. MacKinnon, 2000. "Improving the Reliability of Bootstrap Tests," Working Papers 995, Queen's University, Department of Economics.
  18. Davidson, R. & Mackinnon, J.G., 1996. "The Size Distorsion of Bootstrap Tests," G.R.E.Q.A.M. 96a15, Universite Aix-Marseille III.
  19. James G. MacKinnon, 2006. "Applications of the Fast Double Bootstrap," Working Papers 1023, Queen's University, Department of Economics.
  20. Davidson, James, 2006. "Alternative bootstrap procedures for testing cointegration in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 741-777, August.
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Citations

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Cited by:
  1. Sun, Yixiao & Kim, Min Seong, 2009. "k-step Bootstrap Bias Correction for Fixed Effects Estimators in Nonlinear Panel Models," University of California at San Diego, Economics Working Paper Series qt9gn6n5mr, Department of Economics, UC San Diego.
  2. Patrick Richard, 2008. "Modified Fast Double Sieve Bootstraps for ADF Tests," Cahiers de recherche 08-17, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
  3. Qian, Hang, 2011. "Sampling Variation, Monotone Instrumental Variables and the Bootstrap Bias Correction," MPRA Paper 32634, University Library of Munich, Germany.
  4. Vincent BODART & Bertrand CANDELON & Jean-François CARPANTIER, 2011. "Real Exchange Rates, Commodity Prices and Structural Factors in Developing Countries," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2011045, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  5. Raffaella Giacomini, & Dimitris N. Politis & Halbert White, 2012. "A warp-speed method for conducting Monte Carlo experiments involving bootstrap estimators," CeMMAP working papers CWP11/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Christian Kascha & Carsten Trenkler, 2009. "Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order," Working Paper 2009/12, Norges Bank.
  7. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Papers 1127, Queen's University, Department of Economics.
  8. Cerrato, Mario & Sarantis, Nicholas, 2007. "A bootstrap panel unit root test under cross-sectional dependence, with an application to PPP," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 4028-4037, May.
  9. Riccardo Lucchetti & Claudia Pigini, 2013. "A test for bivariate normality with applications in microeconometric models," Statistical Methods and Applications, Springer, vol. 22(4), pages 535-572, November.
  10. Chiu, Sung Nok & Wang, Ling, 2009. "Homogeneity tests for several Poisson populations," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4266-4278, October.
  11. Ahlgren, N. & Antell, J., 2008. "Bootstrap and fast double bootstrap tests of cointegration rank with financial time series," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4754-4767, June.
  12. Bolduc, Denis & Khalaf, Lynda & Moyneur, Érick, 2008. "Identification-robust simulation-based inference in joint discrete/continuous models for energy markets," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3148-3161, February.
  13. Seojeong Lee, 2014. "Asymptotic Refinements of a Misspecification-Robust Bootstrap for GEL Estimators," Discussion Papers 2014-02, School of Economics, The University of New South Wales.
  14. Kleijnen, J.P.C., 2006. "White Noise Assumptions Revisited: Regression Models and Statistical Designs for Simulation Practice," Discussion Paper 2006-50, Tilburg University, Center for Economic Research.
  15. Godfrey, L.G., 2007. "Alternative approaches to implementing Lagrange multiplier tests for serial correlation in dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3282-3295, April.

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