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Vine copulas constitute a flexible way for modeling of dependences using onlypair copulas as building blocks. The pair-copula constructions introduced byJoe (1997) are able to encode more types of dependences in the same time sincethey can be expressed as a product of different types of bi-variate copulas.The Regular-vine structures (R-vines), as pair copulas corresponding to asequence of trees, have been introduced by Bedford and Cooke (2001, 2002) andfurther explored by Kurowicka and Cooke (2006). The complexity of these modelsstrongly increases in larger dimensions. Therefore the so called truncatedR-vines were introduced in Brechmann et al. (2012). In this paper we expressthe Regular-vines using a special type of hypergraphs, which encodes theconditional independences.

Hypergraphs in the characterization of regular vine copula structures