Granger Causality in Extremes
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 impo...
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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.2407.09632 |