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Properties of Hierarchical Archimedean Copulas

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  • Ostap Okhrin
  • Yarema Okhrin
  • Wolfgang Schmid

Abstract

In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean copulas 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 con¯dence 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.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2009-014.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 SFB649DP2009-014.

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Length: 33 pages
Date of creation: Mar 2009
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2009-014

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Related research

Keywords: copula; multivariate distribution; Archimedean copula; stochastic ordering; hierarchical copula;

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References

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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.
  2. 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.
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Citations

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Cited by:
  1. Roland Strausz, 2010. "The Political Economy of Regulatory Risk," CESifo Working Paper Series 2953, CESifo Group Munich.
  2. Michal Grajek & Lars-Hendrik Röller, 2009. "Regulation and Investment in Network Industries: Evidence from European Telecoms," ESMT Research Working Papers ESMT-09-004, ESMT European School of Management and Technology.
  3. Barbara Choroś & Wolfgang Härdle & Ostap Okhrin, 2009. "CDO and HAC," SFB 649 Discussion Papers SFB649DP2009-038, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Maria Grith & Wolfgang Härdle & Juhyun Park, 2009. "Shape invariant modelling pricing kernels and risk aversion," SFB 649 Discussion Papers SFB649DP2009-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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