Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls

CentER Discussion Paper Series No. 2006-29

11 Pages Posted: 9 May 2006  

Arthur Charpentier

National Institute of Statistics and Economic Studies (INSEE) - National School for Statistical and Economic Administration (ENSAE)

Johan Segers

Catholic University of Louvain (UCL)

Date Written: April 2006

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.

Keywords: Archimedean copula, regular variation, tail dependence, de Haan class

JEL Classification: C14, C16

Suggested Citation

Charpentier, Arthur and Segers, Johan, Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls (April 2006). CentER Discussion Paper Series No. 2006-29. Available at SSRN: https://ssrn.com/abstract=900114 or http://dx.doi.org/10.2139/ssrn.900114

Arthur Charpentier (Contact Author)

National Institute of Statistics and Economic Studies (INSEE) - National School for Statistical and Economic Administration (ENSAE) ( email )

92245 Malakoff Cedex
France

Johan Segers

Catholic University of Louvain (UCL) ( email )

Place Montesquieu, 3
Louvain-la-Neuve, 1348
Belgium
+32 10 474311 (Phone)
+32 10 473032 (Fax)

HOME PAGE: http://www.uclouvain.be/stat

Paper statistics

Downloads
262
Rank
96,296
Abstract Views
1,237