Time series clustering on lower tail dependence for portfolio selection

In this paper we analyse a case study based on the procedure introduced by De Luca and Zuccolotto (2011), whose aim is to cluster time series of financial returns in groups being homogeneous in the sense that their joint bivariate distributions exhibit high association in the lower tail. The dissimilarity measure used for such clustering is based on tail dependence coefficients estimated using copula functions. We carry out the clustering using an algorithm requiring a preliminary transformation of the dissimilarity index into a distance metric by means of a geometric representation of the time series, obtained with Multidimensional Scaling. We show that the results of the clustering can be used for a portfolio selection purpose, when the goal is to protect investments from the effects of a financial crisis.