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Fitting high-dimensional copulae to data

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  • Okhrin, Ostap

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.

Suggested Citation

  • Okhrin, Ostap, 2010. "Fitting high-dimensional copulae to data," SFB 649 Discussion Papers 2010-022, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2010-022
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    1. 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.
    2. 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.
    3. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
    4. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 130-168.
    5. 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.
    6. Wei Xu & Guenther Filler & Martin Odening & Ostap Okhrin, 2010. "On the systemic nature of weather risk," Agricultural Finance Review, Emerald Group Publishing Limited, vol. 70(2), pages 267-284, August.
    7. Chen, Xiaohong & Fan, Yanqin & Patton, Andrew J., 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.
    8. Jean-David FERMANIAN & Olivier SCAILLET, 2003. "Nonparametric Estimation of Copulas for Time Series," FAME Research Paper Series rp57, International Center for Financial Asset Management and Engineering.
    9. Giacomini, Enzo & Härdle, Wolfgang Karl & Ignatieva, Ekaterina & Spokoiny, Vladimir, 2006. "Inhomogeneous dependency modelling with time varying copulae," SFB 649 Discussion Papers 2006-075, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    10. 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.
    11. Okhrin, Ostap & Okhrin, Yarema & Schmid, Wolfgang, 2009. "Properties of hierarchical Archimedean copulas," SFB 649 Discussion Papers 2009-014, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    12. David A. Hennessy & Harvey E. Lapan, 2002. "The Use of Archimedean Copulas to Model Portfolio Allocations," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 143-154, April.
    13. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    14. Wei Xu & Guenther Filler & Martin Odening & Ostap Okhrin, 2010. "On the systemic nature of weather risk," Agricultural Finance Review, Emerald Group Publishing Limited, vol. 70(2), pages 267-284, August.
    15. 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, June.
    16. 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.
    17. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    18. 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.
    19. 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.
    20. Okhrin Ostap & Okhrin Yarema & Schmid Wolfgang, 2013. "Properties of hierarchical Archimedean copulas," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 21-54, March.
    21. Niall Whelan, 2004. "Sampling from Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 339-352.
    22. Markus Junker & Angelika May, 2005. "Measurement of aggregate risk with copulas," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 428-454, December.
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    More about this item

    Keywords

    copula; multivariate distribution; Archimedean copula; GoF;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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