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Fitting high-dimensional Copulae to Data

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  • Ostap Okhrin

Abstract

This paper make an overview of the copula theory from a practical side. We consider different methods of copula estimation and different Goodness-of-Fit tests for model selection. In the GoF section we apply Kolmogorov-Smirnov and Cramer-von-Mises type tests and calculate power of these tests under different assumptions. Novating in this paper is that all the procedures are done in dimensions higher than two, and in comparison to other papers we consider not only simple Archimedean and Gaussian copulae but also Hierarchical Archimedean Copulae. Afterwards we provide an empirical part to support the theory.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2010-022.pdf
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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2010-022.

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Length: 34 pages
Date of creation: Apr 2010
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2010-022

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Keywords: copula; multivariate distribution; Archimedean copula; GoF;

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References

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  1. Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2004. "Efficient Estimation of Semiparametric Multivariate Copula Models," Vanderbilt University Department of Economics Working Papers 0420, Vanderbilt University Department of Economics.
  2. Wei Xu & Guenther Filler & Martin Odening & Ostap Okhrin, 2010. "On the systemic nature of weather risk," Agricultural Finance Review, Emerald Group Publishing, vol. 70(2), pages 267-284, August.
  3. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
  4. Giacomini, Enzo & Härdle, Wolfgang & Spokoiny, Vladimir, 2009. "Inhomogeneous Dependence Modeling with Time-Varying Copulae," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 224-234.
  5. Xiaohong Chen & Yanqin Fan & Andrew J. Patton, 2004. "Simple tests for models of dependence between multiple financial time series, with applications to U.S. equity returns and exchange rates," LSE Research Online Documents on Economics 24681, London School of Economics and Political Science, LSE Library.
  6. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
  7. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 130-168.
  8. Christian Genest & Jean-François Quessy & Bruno Rémillard, 2006. "Goodness-of-fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 33(2), pages 337-366.
  9. W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 1-14.
  10. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
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  12. Cornelia Savu & Mark Trede, 2008. "Goodness-of-fit tests for parametric families of Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 109-116.
  13. Genest, Christian & Rivest, Louis-Paul, 1989. "A characterization of gumbel's family of extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 207-211, August.
  14. Hennessy, David A. & Lapan, Harvey E., 2002. "Use of Archimedean Copulas to Model Portfolio Allocations, The," Staff General Research Papers 5223, Iowa State University, Department of Economics.
  15. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
  16. Markus Junker & Angelika May, 2005. "Measurement of aggregate risk with copulas," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 428-454, December.
  17. Lee, Tae-Hwy & Long, Xiangdong, 2009. "Copula-based multivariate GARCH model with uncorrelated dependent errors," Journal of Econometrics, Elsevier, vol. 150(2), pages 207-218, June.
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Cited by:
  1. Maria Grith & Volker Krätschmer, 2010. "Parametric estimation of risk neutral density functions," SFB 649 Discussion Papers SFB649DP2010-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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