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Goodness-of-fit tests for copulas: A review and a power study

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  • Genest, Christian
  • Rémillard, Bruno
  • Beaudoin, David

Abstract

Many proposals have been made recently for goodness-of-fit testing of copula models. After reviewing them briefly, the authors concentrate on "blanket tests", i.e., those whose implementation requires neither an arbitrary categorization of the data nor any strategic choice of smoothing parameter, weight function, kernel, window, etc. The authors present a critical review of these procedures and suggest new ones. They describe and interpret the results of a large Monte Carlo experiment designed to assess the effect of the sample size and the strength of dependence on the level and power of the blanket tests for various combinations of copula models under the null hypothesis and the alternative. To circumvent problems in the determination of the limiting distribution of the test statistics under composite null hypotheses, they recommend the use of a double parametric bootstrap procedure, whose implementation is detailed. They conclude with a number of practical recommendations.

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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 44 (2009)
Issue (Month): 2 (April)
Pages: 199-213

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Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:199-213

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Web page: http://www.elsevier.com/locate/inca/505554

Related research

Keywords: Anderson-Darling statistic Copula Cramér-von Mises statistic Gaussian process Goodness-of-fit Kendall's tau Kolmogorov-Smirnov statistic Monte Carlo simulation Parametric bootstrap Power study Pseudo-observations P-values;

References

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  1. Scaillet, Olivier, 2007. "Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 98(3), pages 533-543, March.
  2. Tomasz Burzykowski & Geert Molenberghs & Marc Buyse, 2004. "The validation of surrogate end points by using data from randomized clinical trials: a case-study in advanced colorectal cancer," Journal of the Royal Statistical Society Series A, Royal Statistical Society, Royal Statistical Society, vol. 167(1), pages 103-124.
  3. Yannick Malevergne & Didier Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Post-Print, HAL hal-00520539, HAL.
  4. Thierry Ane & Cecile Kharoubi, 2003. "Dependence Structure and Risk Measure," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 76(3), pages 411-438, July.
  5. Markus Junker & Angelika May, 2005. "Measurement of aggregate risk with copulas," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 8(3), pages 428-454, December.
  6. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
  7. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 82(1), pages 1-16, July.
  8. Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2004. "Efficient Estimation of Semiparametric Multivariate Copula Models," Vanderbilt University Department of Economics Working Papers, Vanderbilt University Department of Economics 0420, Vanderbilt University Department of Economics.
  9. W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 3(1), pages 1-14.
  10. Klugman, Stuart A. & Parsa, Rahul, 1999. "Fitting bivariate loss distributions with copulas," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 24(1-2), pages 139-148, March.
  11. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 94(2), pages 401-419, June.
  12. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 51(6), pages 2836-2850, March.
  13. Panchenko, Valentyn, 2005. "Goodness-of-fit test for copulas," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 355(1), pages 176-182.
  14. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 95(1), pages 119-152, July.
  15. Frahm, Gabriel & Junker, Markus & Szimayer, Alexander, 2003. "Elliptical copulas: applicability and limitations," Statistics & Probability Letters, Elsevier, Elsevier, vol. 63(3), pages 275-286, July.
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