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The regular variation model for multivariate extremes decomposes the jointdistribution of the extremes in polar coordinates in terms of the angles andthe norm of the random vector as the product of two independent densities: theangular (spectral) measure and the density of the norm. The support of theangular measure is the surface of a unit hypersphere and the density of thenorm corresponds to a Pareto density. The dependence structure is determined bythe angular measure on the hypersphere, and directions with high probabilitycharacterize the dependence structure among the elements of the random vectorof extreme values. Previous applications of the regular variation model havenot considered a probabilistic model for the angular density and no statisticaltests were applied. In this paper, circular and spherical distributions basedon nonnegative trigonometric sums are considered flexible probabilistic modelsfor the spectral measure that allows the application of statistical tests tomake inferences about the dependence structure among extreme values. Theproposed methodology is applied to real datasets from finance.

Testing the Regular Variation Model for Multivariate Extremes with Flexible Circular and Spherical Distributions