A note on upper-patched generators for Archimedean copulas

Elena Di Bernardino (1) , Didier Rullière (2)

1 CEDRIC - MSDMA - CEDRIC. Méthodes statistiques de data-mining et apprentissage
2 SAF - Laboratoire de Sciences Actuarielle et Financière

The class of multivariate Archimedean copulas is defined by using a real-valued function called the generator of the copula. This generator satisfies some properties, including d-monotony. We propose here a new basic transformation of this generator, preserving these properties, thus ensuring the validity of the transformed generator and inducing a proper valid copula. This transformation acts only on a specific portion of the generator, it allows both the non-reduction of the likelihood on a given dataset, and the choice of the upper tail dependence coefficient of the transformed copula. Numerical illustrations show the utility of this construction, which can improve the fit of a given copula both on its central part and its tail.

Mots clés: Archimedean copulas; transformations; distortions; tail dependence coefficients; likelihood

Domaines: Economies et finances; Probabilités [math.PR]; Statistiques [math.ST]

Elena Di Bernardino, Didier Rullière. A note on upper-patched generators for Archimedean copulas. ESAIM: Probability and Statistics, 2017, ⟨10.1051/ps/2017003⟩. ⟨hal-01347869v2⟩