Explicit Granger causality in kernel Hilbert spaces

TL;DR

This paper introduces a generalized kernel-based Granger causality framework that explicitly models variable cross-relations in Hilbert spaces, improving causal inference in complex dynamical systems and climate phenomena.

Contribution

It extends existing kernel Granger causality methods by explicitly considering cross-relations in Hilbert spaces, with theoretical performance bounds and practical applications.

Findings

Effective in standard dynamical systems

Identifies arrow of time in Rössler systems

Discovers ENSO footprints on global soil moisture

Abstract

Granger causality (GC) is undoubtedly the most widely used method to infer cause-effect relations from observational time series. Several nonlinear alternatives to GC have been proposed based on kernel methods. We generalize kernel Granger causality by considering the variables cross-relations explicitly in Hilbert spaces. The framework is shown to generalize the linear and kernel GC methods, and comes with tighter bounds of performance based on Rademacher complexity. We successfully evaluate its performance in standard dynamical systems, as well as to identify the arrow of time in coupled R\"ossler systems, and is exploited to disclose the El Ni\~no-Southern Oscillation (ENSO) phenomenon footprints on soil moisture globally.