  Regular vine sequences permit the organisation of variables in a random
vector along a sequence of trees. Regular vine models have become greatly
popular in dependence modelling as a way to combine arbitrary bivariate copulas
into higher-dimensional ones, offering flexibility, parsimony, and
tractability. In this project, we use regular vine structures to decompose and
construct the exponent measure density of a multivariate extreme value
distribution, or, equivalently, the tail copula density. Although these
densities pose theoretical challenges due to their infinite mass, their
homogeneity property offers simplifications. The theory sheds new light on
existing parametric families and facilitates the construction of new ones,
called X-vines. Computations proceed via recursive formulas in terms of
bivariate model components. We develop simulation algorithms for X-vine
multivariate Pareto distributions as well as methods for parameter estimation
and model selection on the basis of threshold exceedances. The methods are
illustrated by Monte Carlo experiments and a case study on US flight delay
data.
