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Finite-sample resampling-based combined hypothesis tests, with applications to serial correlation and predictability

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  • Jean-Marie Dufour

    ()

  • Lynda Khalaf
  • Marcel Voia

Abstract

This paper suggests Monte Carlo multiple test procedures which are provably valid in finite samples. These include combination methods originally proposed for independent statistics and further improvements which formalize statistical practice. We also adapt the Monte Carlo test method to non-continuous combined statistics. The methods suggested are applied to test serial dependence and predictability. In particular, we introduce and analyze new procedures that account for endogenous lag selection. A simulation study illustrates the properties of the proposed methods. Results show that concrete and non-spurious power gains (over standard combination methods) can be achieved through the combined Monte Carlo test approach, and confirm arguments in favour of variance-ratio type criteria.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2013s-40.

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Date of creation: 01 Oct 2013
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Handle: RePEc:cir:cirwor:2013s-40

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Keywords: Monte Carlo test; induced test; test combination; simultaneous inference; Variance ratio;

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  1. DUFOUR, Jean-Marie & KHALAF, Lynda & BEAULIEU, Marie-Claude, 2003. "Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-Fit in Multivariate Regressions with Application to Asset Pricing Models," Cahiers de recherche 07-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Deschamps, P. J., . "Monte Carlo methodology for LM and LR autocorrelation tests in multivariate regression," CORE Discussion Papers RP -1234, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, vol. 57(2), pages 335-55, March.
  4. DUFOUR, Jean-Marie & FARHAT, Abdeljelil & GARDIOL, Lucien, 1998. "Simulation-Based Finite-Sample Normality Tests in Linear Regressions," Cahiers de recherche 9811, Universite de Montreal, Departement de sciences economiques.
  5. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
  6. Yilmaz, Kamil, 2003. "Martingale Property of Exchange Rates and Central Bank Interventions," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 383-95, July.
  7. Wright, Jonathan H, 2000. "Alternative Variance-Ratio Tests Using Ranks and Signs," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 1-9, January.
  8. Kim, Jae H., 2006. "Wild bootstrapping variance ratio tests," Economics Letters, Elsevier, vol. 92(1), pages 38-43, July.
  9. Dezhbakhsh, Hashem, 1990. "The Inappropriate Use of Serial Correlation Tests in Dynamic Linear Models," The Review of Economics and Statistics, MIT Press, vol. 72(1), pages 126-32, February.
  10. Jean-Marie Dufour & Abdeljelil Farhat & Lynda Khalaf, 2005. "Tests multiples simulés et tests de normalité basés sur plusieurs moments dans les modèles de régression," CIRANO Working Papers 2005s-05, CIRANO.
  11. Amélie Charles & Olivier Darne, 2009. "Variance ratio tests of random walk: An overview," Post-Print hal-00771078, HAL.
  12. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
  13. Politis, D. N. & Romano, Joseph P. & Wolf, Michael, 1997. "Subsampling for heteroskedastic time series," Journal of Econometrics, Elsevier, vol. 81(2), pages 281-317, December.
  14. Chow, K. Victor & Denning, Karen C., 1993. "A simple multiple variance ratio test," Journal of Econometrics, Elsevier, vol. 58(3), pages 385-401, August.
  15. Zhou, Guofu, 1993. " Asset-Pricing Tests under Alternative Distributions," Journal of Finance, American Finance Association, vol. 48(5), pages 1927-42, December.
  16. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  17. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2007. "Multivariate Tests of MeanVariance Efficiency With Possibly Non-Gaussian Errors: An Exact Simulation-Based Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 398-410, October.
  18. Bernard, Jean-Thomas & Idoudi, Nadhem & Khalaf, Lynda & Yelou, Clement, 2007. "Finite sample multivariate structural change tests with application to energy demand models," Journal of Econometrics, Elsevier, vol. 141(2), pages 1219-1244, December.
  19. Fong, Wai Mun & Koh, Seng Kee & Ouliaris, Sam, 1997. "Joint Variance-Ratio Tests of the Martingale Hypothesis for Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 51-59, January.
  20. Kilian, Lutz & Demiroglu, Ufuk, 2000. "Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 40-50, January.
  21. Whang, Yoon-Jae & Kim, Jinho, 2003. "A multiple variance ratio test using subsampling," Economics Letters, Elsevier, vol. 79(2), pages 225-230, May.
  22. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
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