Wasserstein Dissimilarity for Copula-Based Clustering of Time Series with Spatial Information

The clustering of time series with geo-referenced data requires a suitable dissimilarity matrix interpreting the comovements of the time series and taking into account the spatial constraints. In this paper, we propose a new way to compute the dissimilarity matrix, merging both types of information, which leverages on the Wasserstein distance. We then make a quasi-Gaussian assumption that yields more convenient formulas in terms of the joint correlation matrix. The method is illustrated in a case study involving climatological data.