Extreme event propagation using counterfactual theory and vine copulas

TL;DR

This paper introduces a novel framework combining extreme value theory and vine copulas to analyze how extreme events propagate across related quantities, demonstrated on traffic and air pollution data.

Contribution

It develops an Extreme Event Propagation framework that maximizes counterfactual causation probabilities using advanced statistical tools, offering new insights into extremal dependencies.

Findings

Replicated atmospheric mechanisms beyond linear models

Quantified propagation of traffic and pollution extremes

Provided a flexible tool for various applications

Abstract

Understanding multivariate extreme events play a crucial role in managing the risks of complex systems since extremes are governed by their own mechanisms. Conditional on a given variable exceeding a high threshold (e.g.\ traffic intensity), knowing which high-impact quantities (e.g\ air pollutant levels) are the most likely to be extreme in the future is key. This article investigates the contribution of marginal extreme events on future extreme events of related quantities. We propose an Extreme Event Propagation framework to maximise counterfactual causation probabilities between a known cause and future high-impact quantities. Extreme value theory provides a tool for modelling upper tails whilst vine copulas are a flexible device for capturing a large variety of joint extremal behaviours. We optimise for the probabilities of causation and apply our framework to a London road traffic and air pollutants dataset. We replicate documented atmospheric mechanisms beyond linear relationships. This provides a new tool for quantifying the propagation of extremes in a large variety of applications.