Modeling spatial extremes using normal mean-variance mixtures

TL;DR

This paper introduces a new spatial copula model based on the generalized hyperbolic distribution, capable of capturing both asymptotic dependence and independence in environmental spatial data, with corrected tail dependence analysis.

Contribution

It proposes a novel flexible spatial copula model using the generalized hyperbolic distribution and corrects previous misconceptions about its tail dependence properties.

Findings

Model effectively captures tail and bulk dependence in environmental data

Corrected theoretical tail dependence structure for the generalized hyperbolic distribution

Demonstrated model's applicability on real-world environmental datasets

Abstract

Classical models for multivariate or spatial extremes are mainly based upon the asymptotically justified max-stable or generalized Pareto processes. These models are suitable when asymptotic dependence is present, i.e., the joint tail decays at the same rate as the marginal tail. However, recent environmental data applications suggest that asymptotic independence is equally important and, unfortunately, existing spatial models in this setting that are both flexible and can be fitted efficiently are scarce. Here, we propose a new spatial copula model based on the generalized hyperbolic distribution, which is a specific normal mean-variance mixture and is very popular in financial modeling. The tail properties of this distribution have been studied in the literature, but with contradictory results. It turns out that the proofs from the literature contain mistakes. We here give a corrected theoretical description of its tail dependence structure and then exploit the model to analyze a simulated dataset from the inverted Brown-Resnick process, hindcast significant wave height data in the North Sea, and wind gust data in the state of Oklahoma, USA. We demonstrate that our proposed model is flexible enough to capture the dependence structure not only in the tail but also in the bulk.