Model-based clustering of time-dependent observations with common structural changes

We propose a novel model-based clustering approach for samples of time series. We assume as a unique commonality that two observations belong to the same group if structural changes in their behaviours happen at the same time. We resort to a latent representation of structural changes in each time series based on random orders to induce ties among different observations. Such an approach results in a general modeling strategy and can be combined with many time-dependent models known in the literature. Our studies have been motivated by an epidemiological problem, where we want to provide clusters of different countries of the European Union, where two countries belong to the same cluster if the spreading processes of the COVID-19 virus had structural changes at the same time.