TY - JOUR

T1 - Modeling spatial extremes using normal mean-variance mixtures

AU - Zhang, Zhongwei

AU - Huser, Raphael

AU - Opitz, Thomas

AU - Wadsworth, Jennifer

N1 - The final publication is available at Springer via http://dx.doi.org/10.1111/biom.13581

PY - 2022/6/30

Y1 - 2022/6/30

N2 - 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 equallyimportant 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.

AB - 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 equallyimportant 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.

KW - Asymptotic independence

KW - Copula model

KW - Generalized hyperbolic distribution

KW - Normal mean-variance mixtures

KW - Spatial extremes

U2 - 10.1007/s10687-021-00434-2

DO - 10.1007/s10687-021-00434-2

M3 - Journal article

VL - 25

SP - 175

EP - 197

JO - Extremes

JF - Extremes

SN - 1386-1999

IS - 2

ER -