Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls
AbstractTail 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.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2006-29.
Date of creation: 2006
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Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-04-29 (All new papers)
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ICER Working Papers - Applied Mathematics Series
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