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Properties of hierarchical Archimedean copulas

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  • Okhrin, Ostap
  • Okhrin, Yarema
  • Schmid, Wolfgang

Abstract

In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean opulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula value, which is particularly useful for tests and constructing confidence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures and extreme value copulas. Special attention we pay to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:sfb649:sfb649dp2009-014
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    References listed on IDEAS

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    1. Nelsen, Roger B., 1997. "Dependence and Order in Families of Archimedean Copulas," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 111-122, January.
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    3. Charpentier, Arthur & Segers, Johan, 2009. "Tails of multivariate Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1521-1537, August.
    4. Barbe, Philippe & Genest, Christian & Ghoudi, Kilani & Rémillard, Bruno, 1996. "On Kendall's Process," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 197-229, August.
    5. Niall Whelan, 2004. "Sampling from Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 339-352.
    6. Hofert, Marius, 2008. "Sampling Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5163-5174, August.
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    More about this item

    Keywords

    Copula; multivariate distribution; Archimedean copula; stochastic ordering; hierarchical copula;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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