A0207
Title: Dynamic modeling of extremal dependence in bivariate time series
Authors: Ioannis Papastathopoulos - University of Edinburgh (United Kingdom) [presenting]
Abstract: Accurately understanding how the joint behavior of extreme events changes over time is fundamental for risk assessment across many disciplines. A probabilistic framework is introduced for bivariate time series, leading to a statistical methodology for quantifying this evolving dependence. This approach centers on the framework of geometric extremes, which characterizes extremal dependence by analyzing the limiting behavior of suitably rescaled sample clouds. The statistical methods adapt standard generalized linear models, which employ specific linear predictors constructed from tensor-product combinations of temporal and directional random fields. A key outcome of this framework is the concept of "isotropic return-tubes"-novel sets in direction and time, visited with a prespecified, often arbitrarily small, probability, which balances exceedances across all directions. The developed statistical tools enable the learning of these sets even at very low probabilities, facilitating extrapolation to unseen extreme scenarios.
