Space-time modelling of extreme events

TL;DR

This paper extends max-stable processes to model extreme events in space and time, providing a framework for consistent estimation and illustrating its application to precipitation data.

Contribution

It introduces a space-time extension of Schlather's max-stable model and discusses estimation methods and efficiency considerations.

Findings

Effective pairwise censored likelihood estimation for space-time max-stable models

Application to Swiss hourly precipitation data demonstrates practical utility

Discussion on pair selection improves estimator efficiency

Abstract

Max-stable processes are the natural analogues of the generalized extreme-value distribution for the modelling of extreme events in space and time. Under suitable conditions, these processes are asymptotically justified models for maxima of independent replications of random fields, and they are also suitable for the modelling of joint individual extreme measurements over high thresholds. This paper extends a model of Schlather (2001) to the space-time framework, and shows how a pairwise censored likelihood can be used for consistent estimation under mild mixing conditions. Estimator efficiency is also assessed and the choice of pairs to be included in the pairwise likelihood is discussed based on computations for simple time series models. The ideas are illustrated by an application to hourly precipitation data over Switzerland.