A0679
Title: Extremes extrapolation in time series: Accurate Bayesian inference based on the peaks over threshold method
Authors: David Carl - Bocconi University (Italy) [presenting]
Simone Padoan - Bocconi University (Italy)
Stefano Rizzelli - University of Padova (Italy)
Abstract: A strictly stationary time series is considered with marginal distribution in the domain of attraction of the generalized extreme value (GEV) distribution. Under mild conditions concerning the serial dependence structure, the largest observations after a linear transformation, i.e., the normalized peaks over a threshold, converge in distribution to a generalized Pareto (GP) distribution. This motivates likelihood-based inference using the GP distribution. It is shown that the resulting naive Bayesian approach, treating the observations as independent, will lead to credible intervals that fail to achieve asymptotic correct coverage. An adjustment is proposed to the likelihood to remedy this issue and show that the resulting posterior distributions for the GP parameters and extreme quantiles retain the same contraction rates as under independence while simultaneously allowing for accurate uncertainty estimation. If there is time left, it will be explained how to extend these results in order to achieve dynamic extrapolation of future extremes.
