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Modeling Multivariate Distributions with Continuous Margins Using the copula R Package

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  • Kojadinovic, Ivan
  • Yan, Jun

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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  • Kojadinovic, Ivan & Yan, Jun, 2010. "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i09).
    • Handle: RePEc:jss:jstsof:v:034:i09
    DOI: http://hdl.handle.net/10.18637/jss.v034.i09
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    1. 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.
    2. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    3. 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.
    4. 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.
    5. 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.
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