Tail-dependence clustering of time series with spatial constraints

We introduce a clustering method for time series based on tail dependence. Such a method also considers spatial constraints by means of a suitable procedure merging temporal and spatial dependence via extreme-value copulas. The cluster composition depends on the choice of the hyper-parameter alpha is an element of ( 0 , 1 ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in (0,1)$$\end{document} used to calibrate the contribution of the spatial dependence to the overall dissimilarity. A novel heuristic approach to select alpha \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} based on a suitable connectedness index associated to each cluster of the partition is proposed.