Granger Causality in Extremes

TL;DR

This paper develops a rigorous mathematical framework for detecting Granger causality specifically during extreme events in time series, addressing a gap in existing methods that focus on the entire distribution.

Contribution

It introduces a novel, model-free inference method for causality in extremes, applicable to non-linear, high-dimensional data, and demonstrates superior performance over existing approaches.

Findings

Framework effectively identifies causality during extreme events.

Method outperforms state-of-the-art in accuracy and speed.

Application to financial and weather data reveals meaningful causal links.

Abstract

We introduce a rigorous mathematical framework for Granger causality in extremes, designed to identify causal links from extreme events in time series. Granger causality plays a pivotal role in uncovering directional relationships among time-varying variables. While this notion gains heightened importance during extreme and highly volatile periods, state-of-the-art methods primarily focus on causality within the body of the distribution, often overlooking causal mechanisms that manifest only during extreme events. Our framework is designed to infer causality mainly from extreme events by leveraging the causal tail coefficient. We establish equivalences between causality in extremes and other causal concepts, including (classical) Granger causality, Sims causality, and structural causality. We prove other key properties of Granger causality in extremes and show that the framework is especially helpful under the presence of hidden confounders. We also propose a novel inference method for detecting the presence of Granger causality in extremes from data. Our method is model-free, can handle non-linear and high-dimensional time series, outperforms current state-of-the-art methods in all considered setups, both in performance and speed, and was found to uncover coherent effects when applied to financial and extreme weather observations.