Anisotropic Brown-Resnick space-time processes: estimation and model assessment

TL;DR

This paper extends Brown-Resnick space-time processes to anisotropic structures, providing estimation methods, model assessment tools, and an application to precipitation data, enhancing modeling of extreme spatial-temporal phenomena.

Contribution

It introduces anisotropic Brown-Resnick models with proven estimation consistency, a statistical test for anisotropy, and diagnostic tools for model assessment.

Findings

Strong consistency and asymptotic normality of estimates.

Successful application to precipitation data in Florida.

Development of diagnostic tools and prediction methods.

Abstract

Spatially isotropic max-stable processes have been used to model extreme spatial or space-time observations. One prominent model is the Brown-Resnick process, which has been successfully fitted to time series, spatial data and space-time data. This paper extends the process to possibly anisotropic spatial structures. For regular grid observations we prove strong consistency and asymptotic normality of pairwise maximum likelihood estimates for fixed and increasing spatial domain, when the number of observations in time tends to infinity. We also present a statistical test for isotropy versus anisotropy. We apply our test to precipitation data in Florida, and present some diagnostic tools for model assessment. Finally, we present a method to predict conditional probability fields and apply it to the data.