Statistical Inference for Time Series Extremes based on the Sliding Block Maxima Method

• Applicant: Professor Dr. Axel Bücher
• Subject Area: Mathematics
• Term: from 2021 to 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 465665892

• Final Report Year: 2025

Final Report Abstract

Extreme value statistics is concerned with the statistical analysis of data samples, often collected over time, at extreme levels. Key quantities of interest include quantiles or return levels that exceed the largest observed value, as well as probabilities and return periods of rare events that may not have occurred within the observed sample. Applications of extreme value statistics are widespread, including fields such as finance, insurance, and environmental science. A common approach for statistically analyzing such extreme events is the block maxima method. Recent case-by-case studies have shown that respective estimators can be improved by an approach called ‘the sliding block maxima method’. The aim of this project was to enhance the sliding block maxima toolbox and to deepen our understanding of the mathematical principles that underpin it. In particular, asymptotic theory was developed for general U-statistics based on sliding block maxima, and a novel bootstrap technique was introduced to assess estimation uncertainties. Overall, the findings of this project pave the way for more efficient and accurate analysis of extreme events compared to traditional methods.

Link to the final report

https://doi.org/10.34657/21442

Publications

• Bootstraping Block Maxima Estimators. Version 1.00
  Staud, T.
  
• Limit theorems for non-degenerate U-statistics of block maxima for time series. Electronic Journal of Statistics, 18(2).
  Bücher, Axel & Staud, Torben
  
• Bootstrapping estimators based on the block maxima method. Journal of the Royal Statistical Society Series B: Statistical Methodology.
  Bücher, Axel & Staud, Torben
  
• On the maximal correlation coefficient for the bivariate Marshall Olkin distribution. Statistics & Probability Letters, 219, 110323.
  Bücher, Axel & Staud, Torben
  
• “On the sliding block maxima method in extreme value statistics”. Doctor- ¨ ¨ althesis. Ruhr-Universitat Bochum, Universitatsbibliothek, 128 pages
  Staud, T.