A2060
Title: Mastering extremes in time series
Authors: Clara Cordeiro - Center for Research and Development in Mathematics and Applications (CIDMA) (Portugal) [presenting]
M Manuela Neves - ISA/ULisboa and CEAUL (Portugal)
Dora Prata Gomes - NOVA.ID.FCT (Portugal)
Pablo Montero Manso - University of Sydney (Australia)
Abstract: Extreme events in univariate time series present major challenges in applications such as river flow modelling, financial risk assessment, and water consumption analysis. Classical forecasting models often fail to adequately capture tail behaviour, leading to poor prediction of rare observations. Extreme Value Theory (EVT) provides a rigorous framework for modelling such extremes. A hybrid methodology is proposed in which a standard forecasting model is first fitted to the time series, and the residuals are then fitted using EVT-based distributions. Particular emphasis is placed on estimating tail characteristics using bootstrap methods to estimate the shape parameter, enabling a more robust representation of extreme behaviour in dependent data. Bootstrap methods are explored and compared across real-data applications, while numerical experiments demonstrate the effectiveness of the proposed framework in improving the modelling and prediction of extreme events. The benefits of combining classical time series forecasting, EVT, and bootstrap-based inference for rare-event analysis are highlighted.
