The course constitutes the 4EU+ alliance Fragship 3 summer school 2023. It is also supported by the CNRS IRN MaDeF.

It will take place at the University of Copenhagen.

Description

The understanding of the appearance of extremes in real-life time series (such as weather and climate observations, returns of stock prices, exchange rates, and stock indices, insurance claim data, failures in energy and social networks) requires suitable probabilistic models and their statistical analyses. Over the last 15-20 years such models and statistical tools have been developed under the assumption of serial dependence. They supplement classical extreme value analysis which deals with independent data.

The goals of the course are

1. to introduce and discuss the recent developments of extreme value theory in the time series context. The main focus will be on heavy-tail phenomena, where extremes are particularly severe, and clustering effects when extremes appear in clumps, 
2. to provide suitable statistical tools for analyzing the aforementioned phenomena,
3. to provide relevant knowledge to graduate students about extreme behavior of random systems in contrast to their average behavior, 
4. to learn about applications of extreme value theory from top experts in the field.

The course aims at PhD and advanced Master's students in statistics, probability theory, and econometrics, or with a background in the aforementioned areas such as physics, and geosciences.

The course corresponds to 2 ECTS. The participants are expected to have a background in probability theory, applied stochastic processes, and statistics.