Extrapolation of max-stable random fields with Fr\'echet marginals

Vitalii Makogin; Evgeny Spodarev; Ilja Sukhanov

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arXiv · 2604.16206

Extrapolation of max-stable random fields with Fr\'echet marginals

Vitalii Makogin·Evgeny Spodarev·Ilja Sukhanov

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Abstract

We propose a method for the prediction of stationary max--stable random fields with $\alpha$-Fr\'echet marginal distribution $H_\alpha$. The method is suitable to cope with heavy tails for $\alpha\in(0,2)$ and is (approximately) exact in marginal distributions. It is based on a recent extrapolation approach via level sets which requires no moment assumptions. An explicit connection between the excursion metric and the Davis-Resnick distance is established. The existence of the predictor is proven. The non-uniqueness of the forecast is demonstrated on several examples. The method is tested on multiple simulated time series and random fields as well as applied to real data of annual maximum precipitation.

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BibTeX RIS

Vitalii Makogin, Evgeny Spodarev, Ilja Sukhanov. 2026-04-17. Extrapolation of max-stable random fields with Fr\'echet marginals. https://arxiv.org/abs/2604.16206

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