Some aspects of extreme value theory under serial dependence

TL;DR

This paper reviews key aspects of extreme value theory for dependent time series, emphasizing residual analysis and the extremal index as a measure of serial extremal dependence, inspired by Laurens de Haan's contributions.

Contribution

It compares marginal tail analysis with residual-based methods and highlights the significance of the extremal index in modeling serial dependence.

Findings

Residual analysis can complement direct tail estimation.

The extremal index effectively measures serial extremal dependence.

Stochastic recurrence equations illustrate extremal dependence concepts.

Abstract

On the occasion of Laurens de Haan's 70th birthday, we discuss two aspects of the statistical inference on the extreme value behavior of time series with a particular emphasis on his important contributions. First, the performance of a direct marginal tail analysis is compared with that of a model-based approach using an analysis of residuals. Second, the importance of the extremal index as a measure of the serial extremal dependence is discussed by the example of solutions of a stochastic recurrence equation.