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Explicit Granger causality in kernel Hilbert spaces

Diego Bueso*, Maria Piles, and Gustau Camps-Valls

  • Image Processing Laboratory (IPL), Universitat de València, 46010 València, Spain

  • *diego.bueso@uv.es
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Phys. Rev. E 102, 062201 – Published 2 December, 2020

DOI: https://doi.org/10.1103/PhysRevE.102.062201

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 Rössler systems, and it is exploited to disclose the El Niño–Southern Oscillation phenomenon footprints on soil moisture globally.

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Phys. Rev. E 102, 062201– Published 2 December, 2020
  • Received 14 May 2020
  • Accepted 28 October 2020
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