Risk forecasting in the context of time series (Q2304433)

The paper focuses on forecasting risk contained in future observations in a time series, considering both the shape parameter and the extremal index of the data. After reviewing the existing approaches to risk forecasting, the authors suggest a novel methodology that considers both the marginal tail and the dependence between risks into account. Then, the assumptions on the model are clearly defined and the parameter estimation is provided. Finally the procedure presented in the paper is applied to forecast future risk to both simulated and real-world data sets; in particular, simulated data are considered to test the performance of the new procedure on the basis of a comparison between the estimated extremal level values and the theoretical benchmark. Some technical details are discussed throughout the appendix concluding the paper.