A0366
Title: Statistical prediction of peaks over a threshold
Authors: Stefano Rizzelli - University of Padova (Italy) [presenting]
Simone Padoan - Bocconi University (Italy)
Abstract: In many applied fields, the prediction of more severe events than those already recorded is crucial for safeguarding against potential future calamities. What-if analyses, which evaluate hypothetical scenarios, play a key role in assessing the potential impacts of extreme events and in guiding the development of effective safety policies. These problems can be tackled using extreme value theory. The well-established peaks-over-threshold method is employed, and a comprehensive toolkit is described to address forecasting needs. An out-of-sample variable is examined, and the focus is on its conditional probability of exceeding a high threshold. Conditions are given under which the generalized Pareto approximation of the corresponding predictive density is accurate, and a Bayesian approach is described for its estimation, enabling the derivation of predictive intervals. By leveraging threshold stability, it is illustrated how predictions can be reliably extended deep into the tail of the unknown data distribution. Asymptotic accuracy of the proposed estimator and predictive intervals is established, as well as that of estimators of notable risk measures based on point forecasts. Finally, the prediction framework is extended to the case of independent data with covariates within a proportional tail model, and to the case of linear time series.
