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Modeling Multivariate Distributions with Continuous Margins Using the copula R Package

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  • Ivan Kojadinovic
  • Jun Yan
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    Abstract

    The copula-based modeling of multivariate distributions with continuous margins is presented as a succession of rank-based tests: a multivariate test of randomness followed by a test of mutual independence and a series of goodness-of-fit tests. All the tests under consideration are based on the empirical copula, which is a nonparametric rank-based estimator of the true unknown copula. The principles of the tests are recalled and their implementation in the copula R package is briefly described. Their use in the construction of a copula model from data is thoroughly illustrated on real insurance and financial data.

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    File URL: http://www.jstatsoft.org/v34/i09/paper
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    Bibliographic Info

    Article provided by American Statistical Association in its journal Journal of Statistical Software.

    Volume (Year): 34 ()
    Issue (Month): i09 ()
    Pages:

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    Handle: RePEc:jss:jstsof:34:i09

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    Web page: http://www.jstatsoft.org/

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    References

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    1. Bruno Rémillard & Olivier Scaillet, 2006. "Testing For Equality Between Two Copulas," Swiss Finance Institute Research Paper Series 07-24, Swiss Finance Institute.
    2. 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.
    3. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    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. Ghoudi, Kilani & Kulperger, Reg J. & Rémillard, Bruno, 2001. "A Nonparametric Test of Serial Independence for Time Series and Residuals," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 191-218, November.
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    Cited by:
    1. Elena Di Bernardino & Didier Rullière, 2013. "On certain transformation of Archimedean copulas: Application to the non-parametric estimation of their generators," Post-Print hal-00834000, HAL.
    2. Kojadinovic, Ivan & Yan, Jun, 2010. "Comparison of three semiparametric methods for estimating dependence parameters in copula models," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 52-63, August.
    3. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2013. "Analyzing the dependence structure of various sectors in the Brazilian market: A Pair Copula Construction approach," Economic Modelling, Elsevier, vol. 35(C), pages 199-206.
    4. Fang, Y. & Madsen, L., 2013. "Modified Gaussian pseudo-copula: Applications in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 292-301.
    5. Ostap Okhrin & Alexander Ristig, 2012. "Hierarchical Archimedean Copulae: The HAC Package," SFB 649 Discussion Papers SFB649DP2012-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2011. "Extreme values dependence of risk in Latin American markets," Economics Bulletin, AccessEcon, vol. 31(4), pages 2903-2914.
    7. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2012. "Evolution of coupled lives' dependency across generations and pricing impact," Carlo Alberto Notebooks 258, Collegio Carlo Alberto.
    8. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2013. "Estimating non-linear serial and cross-interdependence between financial assets," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 837-846.
    9. Elena Di Bernardino & Didier Rullière, 2014. "Estimation of multivariate critical layers: Applications to hydrological data," Working Papers hal-00940089, HAL.
    10. Bologov , Yaroslav, 2013. "A copula-based approach to portfolio credit risk modeling," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 29(1), pages 45-66.
    11. Bellini, Tiziano, 2013. "Integrated bank risk modeling: A bottom-up statistical framework," European Journal of Operational Research, Elsevier, vol. 230(2), pages 385-398.

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