Copula and semicopula transforms

“…Such transformations often manifest in different applied fields. Their action on copulas was studied in [5], and, then, in [2] and in [3] also for semi-copulas.…”

Section: Accepted Manuscript 1 Introductionmentioning

confidence: 99%

On a class of transformations of copulas and quasi-copulas

Alvoni

Papini

Spizzichino

2009

Fuzzy Sets and Systems

View full text Add to dashboard Cite

“…Many types of transformations of copulas have been considered, see for example Valdez and Xiao (2011) or Michiels and De Schepper (2012) for a review of some existing transforms. Transformations of bivariate copula, semicopulas and quasi-copulas are studied in Durante and Sempi (2005). Klement et al (2005a) and Klement et al (2005b) focused on transformations of bivariate Archimax copulas.…”

Section: Transformations On [0 1]mentioning

confidence: 99%

“…Valdez and Xiao (2011) or Michiels and De Schepper (2012) for a review of some existing transforms. See also Durante and Sempi (2005), Klement et al (2005a) and Klement et al (2005b), for transformations in the bivariate case. For transformations based on mixtures, see e.g.…”

Section: Introductionmentioning

confidence: 99%

On tail dependence coefficients of transformed multivariate Archimedean copulas

Bernardino¹,

Rullière²

2016

Fuzzy Sets and Systems

View full text Add to dashboard Cite

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). 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 (2013a) and Di Bernardino and Rullière (2013b). 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. Furthermore, using results in Larsson and Nešlehová (2011), we detail the extreme behaviour of the transformed radial part of Archimedean copulas. At last, we explain possible applications with Markov chains with specific dependence structure.

show abstract

“…For further aspects of the concept of semi-copula and of transformations that will be considered in this paper see also [2,6], and references cited therein.…”

Section: Article In Pressmentioning

confidence: 99%