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The SARS-Cov-2 has spread differently over space and time worldwide. By monitoring the contagion’s time evolution, the November 3 2020 the Italian government introduced differentiated regime of restrictions among its regions. This experiment demonstrated that public health policies can be effectively designed by means of clustering. This paper proposes a fuzzy clustering model where spatial and temporal dimensions of the disease spread are optimally weighted. The resulting model is applied with the aim of identifying groups of Italian regions with similar contagion spread. We found that two groups of regions sharing similar patterns of COVID-19 spread over both space and time exist. Appropriate public health policies can be designed on the basis of this evidence.

The goal of clustering is to identify common structures in a data set by forming groups of homogeneous objects. The observed characteristics of many economic time series motivated the development of classes of distributions that can accommodate properties, such as heavy tails and skewness. Thanks to its flexibility, the skewed exponential power distribution (also called skewed generalized error distribution) ensures a unified and general framework for clustering possibly skewed and heavy tailed time series. This paper develops a clustering procedure of model-based type, assuming that the time series are generated by the same underlying probability distribution but with different parameters. Moreover, we propose to optimally combine the estimated parameters to form the clusters with an entropy weighing k-means approach. The usefulness of the proposal is shown by means of application to financial time series, demonstrating also how the obtained clusters can be used to form portfolio of stocks.