  The regular variation model for multivariate extremes decomposes the joint
distribution of the extremes in polar coordinates in terms of the angles and
the norm of the random vector as the product of two independent densities: the
angular (spectral) measure and the density of the norm. The support of the
angular measure is the surface of a unit hypersphere and the density of the
norm corresponds to a Pareto density. The dependence structure is determined by
the angular measure on the hypersphere, and directions with high probability
characterize the dependence structure among the elements of the random vector
of extreme values. Previous applications of the regular variation model have
not considered a probabilistic model for the angular density and no statistical
tests were applied. In this paper, circular and spherical distributions based
on nonnegative trigonometric sums are considered flexible probabilistic models
for the spectral measure that allows the application of statistical tests to
make inferences about the dependence structure among extreme values. The
proposed methodology is applied to real datasets from finance.
