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Granger Causality and Transfer Entropy Are Equivalent for Gaussian Variables

Lionel Barnett, Adam B. Barrett, and Anil K. Seth
Phys. Rev. Lett. 103, 238701 – Published 4 December 2009
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Abstract

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience. More recently transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, has gained traction in a similarly wide field. While it has been recognized that the two concepts must be related, the exact relationship has until now not been formally described. Here we show that for Gaussian variables, Granger causality and transfer entropy are entirely equivalent, thus bridging autoregressive and information-theoretic approaches to data-driven causal inference.

  • Received 23 October 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.238701

©2009 American Physical Society

Authors & Affiliations

Lionel Barnett*

  • Centre for Computational Neuroscience and Robotics, School of Informatics, University of Sussex, Brighton BN1 9QJ, United Kingdom

Adam B. Barrett† and Anil K. Seth‡

  • Sackler Centre for Consciousness Science, School of Informatics, University of Sussex, Brighton BN1 9QJ, United Kingdom

  • *L.C.Barnett@sussex.ac.uk
  • †abb22@sussex.ac.uk
  • ‡A.K.Seth@sussex.ac.uk

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Issue

Vol. 103, Iss. 23 — 4 December 2009

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