# Modelling non-stationary extremal dependence through a geometric approach

arXiv: https://arxiv.org/abs/2509.22501 · HTML: https://mlsanity.com/paper/2509.22501/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 60 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 19 of 19)

- [Fast calibrated additive quantile regression](https://mlsanity.com/paper/1707.03307/) (2017)
- [Smoothing parameter and model selection for general smooth models](https://mlsanity.com/paper/1511.03864/) (2015)
- [Modeling of spatial extremes in environmental data science: Time to move away from max-stable processes](https://mlsanity.com/paper/2401.17430/) (2024)
- [Determining the Dependence Structure of Multivariate Extremes](https://mlsanity.com/paper/1809.01606/) (2018)
- [Extremal Quantile Regression: An Overview](https://mlsanity.com/paper/1612.06850/) (2016)
- [Modeling spatial processes with unknown extremal dependence class](https://mlsanity.com/paper/1703.06031/) (2017)
- [qgam: Bayesian non-parametric quantile regression modelling in R](https://mlsanity.com/paper/2007.03303/) (2020)
- [Modelling across extremal dependence classes](https://mlsanity.com/paper/1408.5060/) (2014)
- [Modeling asymptotically independent spatial extremes based on Laplace random fields](https://mlsanity.com/paper/1507.02537/) (2015)
- [Automated threshold selection and associated inference uncertainty for univariate extremes](https://mlsanity.com/paper/2310.17999/) (2023)
- [Inference for bivariate extremes via a semi-parametric angular-radial model](https://mlsanity.com/paper/2401.07259/) (2024)
- [Generative Machine Learning for Multivariate Angular Simulation](https://mlsanity.com/paper/2504.21505/) (2025)
- [evgam: An R package for Generalized Additive Extreme Value Models](https://mlsanity.com/paper/2003.04067/) (2020)
- [Linking representations for multivariate extremes via a limit set](https://mlsanity.com/paper/2012.00990/) (2020)
- [Statistical inference for multivariate extremes via a geometric approach](https://mlsanity.com/paper/2208.14951/) (2022)
- [Exceedance-based nonlinear regression of tail dependence](https://mlsanity.com/paper/1802.01535/) (2018)
- [Modelling non-stationarity in asymptotically independent extremes](https://mlsanity.com/paper/2203.05860/) (2022)
- [Improving estimation for asymptotically independent bivariate extremes via global estimators for the angular dependence function](https://mlsanity.com/paper/2303.13237/) (2023)
- [Extreme value methods for estimating rare events in Utopia](https://mlsanity.com/paper/2312.09825/) (2023)

## Abstract (arXiv)

Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models are only suited to stationary data. A recent approach to multivariate extreme value modelling uses a geometric framework, whereby extremal dependence features are inferred through the limiting shapes of scaled sample clouds. This framework can capture a wide range of dependence structures, and a variety of inference procedures have been proposed in the stationary setting. In this work, we first extend the geometric framework to the non-stationary setting and outline assumptions to ensure the necessary convergence conditions hold. We then introduce a flexible, semi-parametric modelling framework for obtaining estimates of limit sets in the non-stationary setting. Through rigorous simulation studies, we demonstrate that our proposed framework can capture a wide range of dependence forms and is robust to different model formulations. We illustrate the proposed methods on financial returns data and present several practical uses.