The use of probabilistic models based on copulas in Estimation of Distribution Algorithms (EDAs) has been identi ed as an emerging research trend on these algorithms for continuous domains. By using copulas, the e ect of the dependence structure and the margins in a joint distribution can be represented separately. Consequently, EDAs based on copulas inherit these characteristics and are able t...

Copulas are a useful tool to model multivariate distributions. While there exist various families of bivariate copulas, much less work has been done when the dimension is higher. We propose a class of multivariate copulas based on products of transformed bivariate copulas. The analytical forms of the copulas within this class allow to naturally associate a graphical structure which helps to vis...

In econometrics, many distributions are non-Gaussian. To describe dependence between non-Gaussian variables, it is usually not sufficient to provide their correlation: it is desirable to also know the corresponding copula. There are many different families of copulas; which family shall we use? In many econometric applications, two families of copulas have been most efficient: the Clayton and t...

Two goodness-of-fit tests for copulas are being investigated. The first one deals with the case of elliptical copulas and the second one deals with independent copulas. These tests result from the expansion of the projection pursuit methodology that we will introduce in the present article. This method enables us to determine on which axis system these copulas lie as well as the exact value of ...

It has been shown that vine copulas constructed from bivariate t copulas can provide good fits to multivariate financial asset return data. However, there might be stronger tail dependence of returns in the joint lower tail of assets than the upper tail. To this end, vine copula models with appropriate choices of bivariate reflection asymmetric linking copulas will be used to assess such tail a...

We use a recent characterization of the d-dimensional Archimedean copulas as the survival copulas of d-dimensional simplex distributions (McNeil and Nešlehová (2009)) to construct new Archimedean copula families, and to examine the relationship between their dependence properties and the radial parts of the corresponding simplex distributions. In particular, a new formula for Kendall’s tau is d...

For the study of dynamic dependence structures, we introduce the concept of pseudo-copulas, extending Patton’s (2001a) definition of conditional copulas, and state the equivalent of Sklar’s theorem for pseudo-copulas. We establish asymptotic normality of nonparametric estimators of the pseudo-copulas under strong mixing assumptions, and discuss applications to specification tests. We complement...

The identification of an appropriate multivariate copula for capturing the dependence structure in multivariate data is not straightforward. The reason is because standard multivariate copulas (such as the multivariate Gaussian, Student-t, and exchangeable Archimedean copulas) lack flexibility to model dependence and have other limitations, such as parameter restrictions. To overcome these prob...

The famous Sklar’s theorem (see [54]) allows to build multivariate distributions using a copula and marginal distributions. For the basic theory on copulas see the first chapter ([14]) or the books on copulas by Joe ([32]) and Nelson ([51]). Much emphasis has been put on the bivariate case and in [32] and [51] many examples of bivariate copula families are given. However the class of multivaria...