Local dependence estimation using semiparametric archimedean copulas

Abstract

Abstract:The authors define a new semiparametric Archimedean copula family having a flexible dependence structure. The family's generator is a local interpolation of existing generators. It has locally-defined dependence parameters. The authors present a penalized constrained least-squares method to estimate and smooth these parameters. They illustrate the flexibility of their dependence model in a bivariate survival example.Estimation de la dépendance locale sur base de copules archimédiennes semiparamétriques Résumé : Les auteurs définissent une nouvelle famille de copules archimédiennes semiparamétriques dont la structure de dépendance est flexible. Le générateur de la famille est une interpolation locale de généra-teurs existants. Ses paramètres de dépendance sont définis localement. Les auteurs présentent une méthode de moindres carrés contraints pénalisés permettant l'estimation lisse de ces paramètres. Ils illustrent la flexibilité de leur modèle de dépendance dans un exemple de survie bivariée.

Pair-copulas modeling in finance

“…Copula parameters are usually estimated by maximum likelihood (Joe 1997), but can be obtained via robust and minimum distance estimators (Tsukahara 2005;Mendes et al 2007), or semi-parametrically (Vandenhende and Lambert 2005). Goodness of fit may be assessed visually by means of pp-plots or based on some formal goodness-of-fit (GOF) test, usually based on the minimization of some criterion.…”

Spline approximations to conditional Archimedean copula

“…A (spline‐based) non‐parametric estimate of ϕ ( ⋅ ) was first proposed in Lambert (). Here, we present another formulation with superior properties and embedding the proposal made by Vandenhende & Lambert () where the function g ( ⋅ ) in was piecewise linear. It can be written as where S ( u ) = − log( − log( u )) is the quantile function of the extreme value distribution and is a linear combination of K cubic B‐splines associated to equidistant knots on ( S ( ε ), S (1 − ε )) for a small quantity ε ( = 10 − 6 , say).…”

Dependence structure of conditional Archimedean copulas

“…For a comprehensive introduction on the theoretical aspects of copulas, the reader is referred to the monographs by Joe [8] and Nelsen [13]. Applications of copulas for modeling purposes are to be found in the works of Cherubini and Luciano [3], Vandenhende and Lambert [18] and Hennessy and Lapan [7], among others. For tests of goodnessof-fit for copulas, see [2,5,6].…”