Tail dependence-based fuzzy clustering of financial time series

In this paper, we propose a new fuzzy clustering of time series with entropy regularization. Following a model-based approach, the dissimilarity measure is based on the bivariate lower tail dependence coefficients estimated for each pair of assets using a copula function. We apply the clustering procedure to the time series of price returns of the assets composing the Dow Jones Sustainability Europe Index and to the time series of 23 Morgan Stanley Capital International (MSCI) Developed Markets indices. We identify the classification structures according to the value selected for the exponent α which enters the Fuzzy Silhouette index formula.