Hierarchical time series clustering on tail dependence with linkage based on a multivariate copula approach

Abstract

Time series clustering with a dissimilarity matrix based on tail dependence coefficients estimated by copula functions has been proposed in 2011 by De Luca and Zuccolotto, who used a two-step procedure allowing to resort to the k-means algorithm. The possibility to carry out hierarchical clustering directly on the dissimilarity matrix is still an open issue and the main concerns are relative to the meaning of the most common linkage methods in the context of tail dependence. In this paper, in a multivariate copula approach, we propose a linkage method based on the tail dependence coefficients between the clusters that are agglomerated at each iteration of the hierarchical clustering algorithms.