A1582
Title: Statistical analysis and modelling of extremes in time series
Authors: Clara Cordeiro - FCiencias.ID, Associacao para a Investigacao e Desenvolvimento de Ciencias (Portugal) (Portugal) [presenting]
Dora Prata Gomes - NOVA.ID.FCT FCT-UNL (Portugal)
Celestino Coelho - DM- FCT UAlg (Portugal)
Manuela Neves - FCiencias.ID, Associacao para a Investigacao e Desenvolvimento de Ciencias (Portugal)
Abstract: The statistical analysis of extreme values has gained prominence in studying events such as floods, heatwaves, hurricanes, and sea level rise, among many others. These phenomena have led to the development of special statistical methodologies for their investigation, understanding, and control where feasible. Such events present distinct statistical challenges, requiring a proper characterisation of the tail of the distribution of the variable under study. Extreme value theory (EVT) is the branch of statistics dedicated to modelling these data types. Conventional forecasting methods need to account for these extreme events effectively, as demonstrated by limitations in their extrapolation. A proposed method involves applying a forecasting procedure to the time series and modelling the residuals with a suitable EVT distribution. In addition, the extreme distribution of the residuals is estimated, and bootstrap estimators of the shape parameter are used to enhance the tail behavior of the residual distribution. A simulation study is presented, and a real case study illustrates the contribution to the modelling of extremes in time series analysis.
