Granger Causality in Extremes

Abstract

We propose a 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 understanding directional relationships among time-varying variables. While the task of causal discovery in time series 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 in the presence of hidden confounders. We also propose a novel inference method for detecting the presence of Granger causality in extremes from observational 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 problems. An open-source implementation of our proposed methodology is provided.

Links

Preprint: https://arxiv.org/abs/2407.09632 (PDF)

Dates

First version: October 2024

Recommended citation: Bodik J., Pasche, O. C. (2024). "Granger Causality in Extremes." ArXiv:2407.09632. https://doi.org/10.48550/arXiv.2407.09632
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