Vine copulas are flexible multivariate dependence models, which are built up from a set of bivariate copulas in different hierarchical levels. However, vine copulas have a computational complexity that is increasing quadratically in the number of variables. This complexity can be reduced by focusing on the sub-class of truncated vine copulas, which use only a limited number of hierarchical leve...

Copulas are d–dimensional probability distribution functions that concentrate the probability mass on I (I := [0, 1]) and whose univariate margins are uniformly distributed on I. Such functions have been largely used in multivariate statistical models, due to the fact that they capture the scale-invariant dependence of random vectors [9, 21]. In view of possible applications, methods for obtain...

Recent large scale simulations indicate that a powerful goodness-of-fit test for copulas can be obtained from the process comparing the empirical copula with a parametric estimate of the copula derived under the null hypothesis. A first way to compute approximate p-values for statistics derived from this process consists of using the parametric bootstrap procedure recently thoroughly revisited ...

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 th...

The Hidden Markov Chain (HMC) model considers that the process of unobservable states is a Markov chain. The Pairwise Markov Chain (PMC) model however considers the couple of processes of observations and states as a Markov chain. It has been shown that the PMC model is strictly more general than the HMC one, but retains the ease of processings that made the success of HMC in a number of applic...

It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a d-dimensional copula is that the generator is a d-monotone function. The class of d-dimensional Archimedean copulas is shown to coincide with the class of survival copulas of d-dimensional l1-norm symmetric distributions that place no point mass at the origin. The d-monotone Archimedean copul...

In this paper, we address the issue of estimating the parameters of general multivariate copulas, that is, copulas whose partial derivatives may not exist. To this aim, we consider a weighted least-squares estimator based on dependence coefficients, and establish its consistency and asymptotic normality. The estimator’s performance on finite samples is illustrated on simulations and a real data...

We propose a method to construct a 3-dimensional symmetric function that is radially symmetric, using two symmetric 2-copulas, with one of them being also radially symmetric. We study the properties of the presented construction in some specific cases and provide several examples for different families of copulas.

Smallest and greatest 1-Lipschitz aggregation operators with given diagonal section, opposite diagonal section, and with graphs passing through a single point of the unit cube, respectively, are determined. These results are used to find smallest and greatest copulas and quasi-copulas with these properties (provided they exist).