Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls

A. Charpentier, J.J.J. Segers

Research output: Working paperDiscussion paperOther research output

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Abstract

Tail dependence copulas provide a natural perspective from which one can study the dependence in the tail of a multivariate distribution.For Archimedean copulas with continuously differentiable generators, regular variation of the generator near the origin is known to be closely connected to convergence of the corresponding lower tail dependence copulas to the Clayton copula.In this paper, these characterizations are refined and extended to the case of generators which are not necessarily continuously differentiable.Moreover, a counterexample is constructed showing that even if the generator of a strict Archimedean copula is continuously differentiable and slowly varying at the origin, then the lower tail dependence copulas do not need to converge to the independent copula.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages12
Volume2006-29
Publication statusPublished - 2006

Publication series

NameCentER Discussion Paper
Volume2006-29

Fingerprint

Archimedean Copula
Tail Dependence
Copula
Continuously differentiable
Generator
Regular Variation
Multivariate Distribution
Counterexample
Tail
Converge

Keywords

  • Archimedean copula
  • regular variation
  • tail dependence
  • de Haan class

Cite this

Charpentier, A., & Segers, J. J. J. (2006). Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls. (CentER Discussion Paper; Vol. 2006-29). Tilburg: Econometrics.
Charpentier, A. ; Segers, J.J.J. / Lower Tail Dependence for Archimedean Copulas : Characterizations and Pitfalls. Tilburg : Econometrics, 2006. (CentER Discussion Paper).
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Charpentier, A & Segers, JJJ 2006 'Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls' CentER Discussion Paper, vol. 2006-29, Econometrics, Tilburg.

Lower Tail Dependence for Archimedean Copulas : Characterizations and Pitfalls. / Charpentier, A.; Segers, J.J.J.

Tilburg : Econometrics, 2006. (CentER Discussion Paper; Vol. 2006-29).

Research output: Working paperDiscussion paperOther research output

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Charpentier A, Segers JJJ. Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls. Tilburg: Econometrics. 2006. (CentER Discussion Paper).