Title: Copula-based clustering of dependent variables with application to flood risks
Authors: Roberta Pappada - University of Trieste (Italy) [presenting]
Fabrizio Durante - University of Salento (Italy)
Sebastian Fuchs - University of Salzburg (Austria)
Abstract: In recent years, copula-based measures of association have been exploited to develop clustering methods that can take into account the dependence structure characterizing the underlying data generating process, e.g., when the data objects to cluster are time series. Motivated by the interest in clustering flood data, which are characterized by a number of physical variables (such as flood peak and volume) and collected at specific geographical sites, some dissimilarity measures are proposed to cluster continuous random variables. Such measures are rank-based, hence depend on the copula of the involved random variables and assign the smallest value to two subsets of random variables that are pairwise comonotonic. Two different notions of multivariate comonotonicity for pairs of random vectors are investigated, which correspond to the strongest version of comonotonicity and a weaker notion called $\pi$-comonotonicity. The proposed dissimilarities are embedded into a hierarchical clustering procedure, with the final aim to detect clusters that account for the comovements of random variables. An application to the analysis of flood risks concerning data collected in the Po river basin is presented, along with the results from different simulated scenarios.