Multivariate distribution models with generalized hyperbolic margins

Multivariate generalized hyperbolic distributions represent an attractive family of distributions (with exponentially decreasing tails) for multivariate data modelling. However, in a limited data environment, robust and fast estimation procedures are rare. An alternative class of multivariate distributions (with exponentially decreasing tails) is proposed which comprises affine-linearly transformed random vectors with stochastically independent and generalized hyperbolic marginals. The latter distributions possess good estimation properties and have attractive dependence structures which are explored in detail. In particular, dependencies of extreme events (tail dependence) can be modelled within this class of multivariate distributions. In addition the necessary estimation and random-number generation procedures are provided. Various advantages and disadvantages of both types of distributions are discussed and illustrated via a simulation study.