Models for construction of multivariate dependence - a comparison study

A multivariate data set, which exhibit complex patterns of dependence, particularly in the tails, can be modelled using a cascade of lower-dimensional copulae. In this paper, we compare two such models that differ in their representation of the dependency structure, namely the nested Archimedean construction (NAC) and the pair-copula construction (PCC). The NAC is much more restrictive than the PCC in two respects. There are strong limitations on the degree of dependence in each level of the NAC, and all the bivariate copulas in this construction has to be Archimedean. Based on an empirical study with two different four-dimensional data sets; precipitation values and equity returns, we show that the PCC provides a better fit than the NAC and that it is computationally more efficient. Hence, we claim that the PCC is more suitable than the NAC for hich-dimensional modelling.