Space-time max-stable models with spectral separability

TL;DR

This paper introduces new space-time max-stable models for extreme events that explicitly separate temporal and spatial effects, including Markovian cases with max-autoregressive structures and a proposed inference method.

Contribution

It develops spectral separability in spatio-temporal max-stable models, addressing limitations of previous models by explicitly modeling temporal dynamics and proposing a new inference approach.

Findings

Models successfully decouple space and time effects.

Markovian max-autoregressive models exhibit desirable properties.

Simulation studies validate the proposed inference methodology.

Abstract

Natural disasters may have considerable impact on society as well as on (re)insurance industry. Max-stable processes are ideally suited for the modeling of the spatial extent of such extreme events, but it is often assumed that there is no temporal dependence. Only a few papers have introduced spatio-temporal max-stable models, extending the Smith, Schlather and Brown-Resnick spatial processes. These models suffer from two major drawbacks: time plays a similar role as space and the temporal dynamics is not explicit. In order to overcome these defects, we introduce spatio-temporal max-stable models where we partly decouple the influence of time and space in their spectral representations. We introduce both continuous and discrete-time versions. We then consider particular Markovian cases with a max-autoregressive representation and discuss their properties. Finally, we briefly propose an inference methodology which is tested through a simulation study.