A new graphical tool for copula selection

The selection of copulas is an important aspect of dependence modeling. In many practical applications, only a limited number of copulas is tested, and the modeling applications usually are restricted to the bivariate case. One explanation is the fact that no graphical copula tool exist which allows to assess the goodness-of-fit of a large set of (possible higher dimensional) copula functions at once. This paper pursues to overcome this problem by developing a new graphical tool for the copula selection, based on a statistical analysis technique called ‘principal coordinate analysis’. The advantage is threefold. In the first place, when projecting the empirical copula of a modeling application on a two-dimensional copula space, it allows us to visualize the fit of a whole collection of multivariate copulas at once. Secondly, the visual tool allows to identify ‘search’ directions for potential fit improvements (e.g. through the use of copula transforms). Finally, in the bivariate case the tool makes it also possible to give a two-dimensional visual overview of a large number of known copula families, for a common concordance value, leading to a better understanding and a more efficient use of the different copula families. The practical use of the new graphical tool is illustrated for two two-dimensional and two three-dimensional fitting applications.