In this research work, we propose to assess the dynamic correlation between different mobility indices, measured on a daily basis, and the new cases of COVID-19 in the different Portuguese districts. The analysis is based on global correlation measures, which capture linear and non-linear relationships in time series, in a robust and dynamic way, in a period without significant changes of non-pharmacological measures. The results show that mobility in retail and recreation, grocery and pharmacy, and public transport shows a higher correlation with new COVID-19 cases than mobility in parks, workplaces or residences. It should also be noted that this relationship is lower in districts with lower population density, which leads to the need for differentiated confinement policies in order to minimize the impacts of a terrible economic and social crisis.

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The energy markets have recently undergone important transformations (e.g. deregulation, technological progress, renewable energy deployment and changing energy consumer behaviour) and witnessed a variety of crisis periods, affecting the relationships among energy commodities and their interactions with clean energy indices. This has implications for price discovery, asset allocation and risk management, which requires in-depth analysis to uncover and identify which energy indices (or forms of energy) lead others or are the most influential, while accounting for asymmetry and non-linearity characteristics. To uncover the complex structure of the relationship across the returns of seven different energy commodities and two clean energy stock indices, we apply Granger causality and transfer entropy in both static and dynamic approaches. The results from the Granger causality analysis identify the influence of the other energy products on natural gas, whereas the transfer entropy analysis reveals the importance of WTI oil and the influence of clean energy indices. Diesel is the most influenced energy commodity. A rolling windows analysis confirms those findings and shows evidence of a time-variation that reflects the impacts of crisis periods, especially the pandemic, on the dynamics of relationships.

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