Dynamic modeling of heavy-tailed extreme events with applications to financial and environmental data

Extreme events characterized by heavy-tailed distributions can cause significant damage, resulting in phenomena such as market crashes or flash floods. The present thesis offers contributions on how to monitor the risk associated to such events through time, by adopting a dynamic modeling approach cast into the Extreme Value Theory (EVT) paradigm. This strategy consists in modeling EVT distributions conditional upon past observed extreme values so that at each point in time an indication of risk is available. The first contribution focuses on time-varying tail risk estimation where extreme events are defined as exceedances over a threshold. Since the threshold selection affects tail risk estimates, dynamic extended versions of Generalized Pareto distribution have been developed to lessen the impact of threshold selection. Simulation studies and real data analyses suggest that working with the extended version of the distribution helps capture departures from the Generalized Pareto approximation yielding robust estimates of tail risk. The second contribution integrates the dynamic modeling approach into the environmental context, and aims at studying trends in hourly extreme precipitation. Despite the concern on increasing intensification of hourly precipitation, available statistical models borrow from a regression setting that is not designed to accommodate hourly precipitation characteristics. We propose a dynamic fixed-effects Generalized Pareto model that allows to capture trends in the extreme high quantiles without the need for strong arbitrary model assumptions. The third contribution introduces the concept of financial tail contagion and aims at studying dynamic extreme cross-sectional dependence among risky assets observed for multiple units (e.g., countries). We develop a dynamic Spatial Autoregressive model in the block maxima context, here the spatial dependence is summarized in just a time-varying parameter. Compared to existing EVT-based models, this approach allows to assess global dependence among units in a parsimonious way.