On tail dependence coefficients of transformed multivariate Archimedean copulas

Elena Di Bernardino () and Didier Rulliere ()
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Elena Di Bernardino: CEDRIC - Centre d'études et de recherche en informatique et communications - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - CNAM - Conservatoire National des Arts et Métiers [CNAM]

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Abstract: This paper presents the impact of a class of transformations of copulas in their upper and lower multivariate tail dependence coefficients. In particular we focus on multivariate Archimedean copulas. In the first part of this paper, we calculate multivariate tail dependence coefficients when the generator of the considered copula exhibits some regular variation properties, and we investigate the behaviour of these coefficients in cases that are close to tail independence. This first part exploits previous works of Charpentier and Segers (2009) and extends some results of Juri and Wüthrich (2003) and De Luca and Rivieccio (2012). We also introduce a new Regular Index Function (RIF) exhibiting some interesting properties. In the second part of the paper we analyse the impact in the upper and lower multivariate tail dependence coefficients of a large class of transformations of dependence structures. These results are based on the transformations exploited by Di Bernardino and Rullière (2013). We extend some bivariate results of Durante et al. (2010) in a multivariate setting by calculating multivariate tail dependence coefficients for transformed copulas. We obtain new results under specific conditions involving regularly varying hazard rates of components of the transformation. In the third part, we show the utility of using transformed Archimedean copulas, as they permit to build Archimedean generators exhibiting any chosen couple of lower and upper tail dependence coefficients. The interest of such study is also illustrated through applications in bivariate settings. At last, we explain possible applications with Markov chains with specific dependence structure.

Keywords: Archimedean copulas; tail dependence coefficients; regular variation; transformations of Archimedean copulas. (search for similar items in EconPapers)
Date: 2016
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://hal.science/hal-00992707v2
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Citations: View citations in EconPapers (3)

Published in Fuzzy Sets and Systems, 2016, 284, pp.89--112. ⟨10.1016/j.fss.2015.08.030⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00992707

DOI: 10.1016/j.fss.2015.08.030

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