A0856
Title: Bayesian inference and probabilistic forecasting for the peaks over threshold approach
Authors: Simone Padoan - Bocconi University (Italy) [presenting]
Stefano Rizzelli - Catholic University of Milan (Italy)
Clement Dombry - Universite de Franche Comte (France)
Abstract: The focus is on the Peaks Over Threshold (POT) method, arguably the most popular approach in the univariate extreme values literature. Many useful inferential procedures for estimating extreme events have been developed in the last decades. To the best of our knowledge, the more ambitious and challenging problem of proper probabilistic forecasting of future extremes has received little or no attention to date. A prior distribution that allows handling the issues arising from using the Generalised Pareto distribution as a misspecified model for the inference regarding the POT method is discussed, and the asymptotic theory of the posterior distribution follows from it is investigated. The primary purpose of risk analysis is the prediction of future extreme events. The problem of probabilistic forecasting of future extremes is addressed by adopting the Bayesian paradigm. Starting from our proposed Bayesian procedure, the posterior predictive distribution of a future unobserved excess above a high threshold is specified, and it is shown that it is Wasserstein consistent concerning the true distribution of such an unobserved future observation.
