Clustering extremal dependence structures via Wasserstein distances between angular measures

Abstract: Compound extreme events cause damage out of proportion to their frequency, and grouping random vectors by their joint extremal behaviour is a recurring task in climate science, hydrology, and finance. Classical clustering is driven by typical observations, while existing extremal procedures either summarize dependence by a single coefficient or discretize the simplex in an ad hoc way. We propose a dissimilarity that compares complete angular measures by optimal transport: each angular measure is estimated above a high radial threshold, mapped from the simplex into a Euclidean space of Aitchison coordinates, and compared by the 1-Wasserstein distance. The methodology is fully nonparametric and requires no fitted model. The dissimilarities feed any distance-based clustering algorithm. Under intermediate-threshold asymptotics and mild moment and separation conditions, hierarchical clustering and partitioning around medoids based on them recovers the latent partition with probability tending to one. In simulations, the proposed approach matches established competitors when clusters differ mainly in the strength of extremal dependence and performs substantially better when equal-strength clusters differ in the shape of their angular measures, especially when asymmetry drives the separation. Applications to rain--snowmelt--runoff extremes in Swiss catchments and to extremal co-movement between international equity markets and the US market reveal hydrologically and economically interpretable groups.