Spatial extremal modelling: A case study on the interplay between margins and dependence

TL;DR

This paper investigates how non-stationarity in marginal distributions affects the detection of dependence changes in spatial extreme value models, using a case study on Red Sea sea surface temperature.

Contribution

It provides an in-depth analysis of the interplay between marginal non-stationarity and dependence detection in spatial extremal models, comparing four detrending methods.

Findings

Marginal non-stationarity influences dependence detection.

Different detrending approaches yield varying results.

Non-stationarity in margins can mask or mimic dependence changes.

Abstract

It is no secret that statistical modelling often involves making simplifying assumptions when attempting to study complex stochastic phenomena. Spatial modelling of extreme values is no exception, with one of the most common such assumptions being stationarity in the marginal and/or dependence features. If non-stationarity has been detected in the marginal distributions, it is tempting to try to model this while assuming stationarity in the dependence, without necessarily putting this latter assumption through thorough testing. However, margins and dependence are often intricately connected and the detection of non-stationarity in one feature might affect the detection of non-stationarity in the other. This work is an in-depth case study of this interrelationship, with a particular focus on a spatio-temporal environmental application exhibiting well-documented marginal non-stationarity. Specifically, we compare and contrast four different marginal detrending approaches in terms of our post-detrending ability to detect temporal non-stationarity in the spatial extremal dependence structure of a sea surface temperature dataset from the Red Sea.