Kernel Method for Nonlinear Granger Causality

Daniele Marinazzo, Mario Pellicoro, and Sebastiano Stramaglia
Phys. Rev. Lett. 100, 144103 – Published 11 April 2008

Abstract

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.

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  • Received 16 November 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.144103

©2008 American Physical Society

Authors & Affiliations

Daniele Marinazzo, Mario Pellicoro, and Sebastiano Stramaglia

  • Dipartimento Interateneo di Fisica, Università di Bari, Italy
  • Istituto Nazionale di Fisica Nucleare, Sezione di Bari, Italy
  • TIRES-Center of Innovative Technologies for Signal Detection and Processing, Università di Bari, Italy

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Issue

Vol. 100, Iss. 14 — 11 April 2008

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