Statistical inference for max-stable processes in space and time

TL;DR

This paper develops a statistical inference method for max-stable space-time processes, using pairwise likelihood estimation, and proves its consistency and asymptotic normality, supported by simulation results.

Contribution

It introduces a pairwise likelihood estimation approach for max-stable space-time processes and establishes its theoretical properties.

Findings

Method performs well in simulations.

Estimates are strongly consistent.

Estimates are asymptotically normal.

Abstract

Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit of normalized and scaled pointwise maxima of stationary Gaussian processes that was first introduced by Kabluchko, Schlather and de Haan (2009). This paper deals with statistical inference for max-stable space-time processes that are defined in an analogous fashion. We describe pairwise likelihood estimation, where the pairwise density of the process is used to estimate the model parameters and prove strong consistency and asymptotic normality of the parameter estimates for an increasing space-time dimension, i.e., as the joint number of spatial locations and time points tends to infinity. A simulation study shows that the proposed method works well for these models.