  Regular vine distributions which constitute a flexible class of multivariate
dependence models are discussed. Since multivariate copulae constructed through
pair-copula decompositions were introduced to the statistical community,
interest in these models has been growing steadily and they are finding
successful applications in various fields. Research so far has however been
concentrating on so-called canonical and D-vine copulae, which are more
restrictive cases of regular vine copulae. It is shown how to evaluate the
density of arbitrary regular vine specifications. This opens the vine copula
methodology to the flexible modeling of complex dependencies even in larger
dimensions. In this regard, a new automated model selection and estimation
technique based on graph theoretical considerations is presented. This
comprehensive search strategy is evaluated in a large simulation study and
applied to a 16-dimensional financial data set of international equity, fixed
income and commodity indices which were observed over the last decade, in
particular during the recent financial crisis. The analysis provides
economically well interpretable results and interesting insights into the
dependence structure among these indices.
