Non-stationary max-stable models with an application to heavy rainfall data

TL;DR

This paper introduces a new non-stationary modeling approach for max-stable processes, incorporating covariates into dependence structures, and demonstrates its effectiveness on heavy rainfall data in Germany.

Contribution

It proposes a novel non-stationary framework for max-stable processes using covariates, extending existing models and analyzing their theoretical properties.

Findings

Non-stationary models outperform stationary ones for Southern Germany rainfall data.

The approach successfully captures spatial dependence variations.

Conditional max-stable processes can exhibit both asymptotic dependence and independence.

Abstract

In recent years, parametric models for max-stable processes have become a popular choice for modeling spatial extremes because they arise as the asymptotic limit of rescaled maxima of independent and identically distributed random processes. Apart from few exceptions for the class of extremal-t processes, existing literature mainly focuses on models with stationary dependence structures. In this paper, we propose a novel non-stationary approach that can be used for both Brown-Resnick and extremal-t processes - two of the most popular classes of max-stable processes - by including covariates in the corresponding variogram and correlation functions, respectively. We apply our new approach to extreme precipitation data in two regions in Southern and Northern Germany and compare the results to existing stationary models in terms of Takeuchi's information criterion (TIC). Our results indicate that, for this case study, non-stationary models are more appropriate than stationary ones for the region in Southern Germany. In addition, we investigate theoretical properties of max-stable processes conditional on random covariates. We show that these can result in both asymptotically dependent and asymptotically independent processes. Thus, conditional models are more flexible than classical max-stable models.