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

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

The statistical analysis of time series data at extreme levels is a recurring task in disciplines like finance, insurance, hydrology and climate research. One of the most fundamental and widely applied statistical principles in the field is known as the block maxima method, which consists of dividing the observation period into non-overlapping periods of equal size and restricting attention to the maximum observation in each period (often a year). Respective methods have recently received increasing attention in mathematical statistics, both for the purpose of validating long-standing statistical methodology under less restrictive assumptions and for the purpose of possibly deriving new and more efficient methodology. The latter category comprises the so-called sliding block maxima method, where the underlying blocks used to calculate maxima are allowed to overlap. The method was found to provide more efficient estimators in selected situations. Within this project, we will advance the sliding block maxima method in various directions. First of all, we aim at establishing limit results for u-statistics of sliding block maxima, which shall be applicable for numerous related statistical problems. Next, motivated by the fact that statistical inference is currently restricted to expensive case-by-case analyses, we will investigate universal bootstrap principles like the classical nonparametric bootstrap, the block bootstrap and subsampling for their applicability to sliding block maxima. A final goal is a further relaxation of underlying assumptions which shall comprise certain typical non-stationary data situations occurring in environmental applications.

• DFG Programme: Research Grants