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

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References

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  1. 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.
  2. Niall Whelan, 2004. "Sampling from Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 4(3), pages 339-352.
  3. Nelsen, Roger B., 1997. "Dependence and Order in Families of Archimedean Copulas," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 111-122, January.
  4. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
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Citations

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Cited by:
  1. Barbara Choroś & Wolfgang Härdle & Ostap Okhrin, 2009. "CDO and HAC," SFB 649 Discussion Papers SFB649DP2009-038, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Ostap Okhrin & Alexander Ristig, 2012. "Hierarchical Archimedean Copulae: The HAC Package," SFB 649 Discussion Papers SFB649DP2012-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. 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.
  4. Shulin Zhang, & Ostap Okhrin, & Qian M. Zhou & Peter X.-K. Song, 2013. "Goodness-of-fit Test for Specification of Semiparametric Copula Dependence Models," SFB 649 Discussion Papers SFB649DP2013-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Göran Kauermann & Renate Meyer, 2014. "Penalized marginal likelihood estimation of finite mixtures of Archimedean copulas," Computational Statistics, Springer, Springer, vol. 29(1), pages 283-306, February.
  6. 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.
  7. Roland Strausz, 2010. "The Political Economy of Regulatory Risk," CESifo Working Paper Series 2953, CESifo Group Munich.
  8. Nikolaus Hautsch & Julia Schuamburg & Melanie Schienle, 2012. "Modeling Time-Varying Dependencies between Positive-Valued High-Frequency Time Series," SFB 649 Discussion Papers SFB649DP2012-054, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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