2023/11/20 by Simone A. Padoan, Padoan, S. A., Stefano Rizzelli +1
Earth and Planetary Sciences · Economics, Econometrics and Finance · Engineering · #60G25 #60G70 #62C10 #62G32 #Energy Load and Power Forecasting #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Meteorological Phenomena and Simulations #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.2311.11852
openalex publication_date 2023/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In many applied fields it is desired to make predictions with the aim of assessing the plausibility of more severe events than those already recorded to safeguard against calamities that have not yet occurred. This problem can be analysed using extreme value theory. We consider the popular peaks over a threshold method and show that the generalised Pareto approximation of the true predictive densities of both a future unobservable excess or peak random variable can be very accurate. We propose both a frequentist and a Bayesian approach for the estimation of such predictive densities. We show the asymptotic accuracy of the corresponding estimators and, more importantly, prove that the resulting predictive inference is asymptotically reliable. We show the utility of the proposed predictive tools analysing extreme temperatures in Milan in Italy.