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Improving the reliability of bootstrap tests with the fast double bootstrap

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  • Davidson, Russell
  • MacKinnon, James G.

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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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 51 (2007)
Issue (Month): 7 (April)
Pages: 3259-3281

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Handle: RePEc:eee:csdana:v:51:y:2007:i:7:p:3259-3281

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References

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  1. Davidson, Russell & MacKinnon, James G., 2002. "Bootstrap J tests of nonnested linear regression models," Journal of Econometrics, Elsevier, vol. 109(1), pages 167-193, July.
  2. DUFOUR, Jean-Marie & KHALAF, Lynda & BERNARD, Jean-Thomas, 2001. "Simulation-Based Finite-Sample Tests for Heteroskedasticity and ARCH Effects," Cahiers de recherche 2001-08, Universite de Montreal, Departement de sciences economiques.
  3. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
  4. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
  5. Davidson, Russell & MacKinnon, James G., 2006. "The power of bootstrap and asymptotic tests," Journal of Econometrics, Elsevier, vol. 133(2), pages 421-441, August.
  6. Russell Davidson & James G. MacKinnon, 1982. "Convenient Specification Tests for Logit and Probit Models," Working Papers 514, Queen's University, Department of Economics.
  7. GONÇALVES, Silvia & KILIAN, Lutz, 2003. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Cahiers de recherche 2003-01, Universite de Montreal, Departement de sciences economiques.
  8. 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.
  9. Mackinnon, J.G. & Smith, A.A., 1996. "Approximate Bias Correction in Econometrics," G.R.E.Q.A.M. 96a14, Universite Aix-Marseille III.
  10. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
  11. Davidson, R. & Mackinnon, J.G., 1997. "Bootstrap Testing in Nonlinear Models," G.R.E.Q.A.M. 97a39, Universite Aix-Marseille III.
  12. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  13. James G. MacKinnon, 2006. "Applications of the Fast Double Bootstrap," Working Papers 1023, Queen's University, Department of Economics.
  14. 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.
  15. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
  16. 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.
  17. Russell Davidson & James G. MacKinnon, 2000. "Improving the Reliability of Bootstrap Tests," Working Papers 995, Queen's University, Department of Economics.
  18. Davidson, James, 2006. "Alternative bootstrap procedures for testing cointegration in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 741-777, August.
  19. Jean-FranÁois Lamarche, 2004. "The Numerical Performance of Fast Bootstrap Procedures," Computational Economics, Society for Computational Economics, vol. 23(4), pages 379-389, 06.
  20. 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.
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Citations

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Cited by:
  1. 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.
  2. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(03), pages 567-589, June.
  3. 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.
  4. Kascha, Christian & Trenkler, Carsten, 2011. "Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1008-1017, February.
  5. 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.
  6. 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.
  7. Richard, Patrick, 2009. "Modified fast double sieve bootstraps for ADF tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4490-4499, October.
  8. Vincent Bodart & Bertrand Candelon & Jean-François Carpantier, 2013. "Real exchange rates, commodity prices and structural factors in developing countries," CREA Discussion Paper Series 13-09, Center for Research in Economic Analysis, University of Luxembourg.
  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. 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.
  11. 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.
  12. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Papers 1127, Queen's University, Department of Economics.
  13. Chiu, Sung Nok & Wang, Ling, 2009. "Homogeneity tests for several Poisson populations," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4266-4278, October.
  14. Qian, Hang, 2011. "Sampling Variation, Monotone Instrumental Variables and the Bootstrap Bias Correction," MPRA Paper 32634, University Library of Munich, Germany.
  15. 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.

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