Granger causality is designed to measure effect, not mechanism

Adam B Barrett,Lionel Barnett

doi:10.3389/fninf.2013.00006

Abstract

Granger causality is designed to measure effect, not mechanism

Highlights

Reviewed by: Marc-Oliver Gewaltig, Ecole Polytechnique Federale de Lausanne, Switzerland Athanassia Chalimourda, Ecole Polytechnique Federale de Lausanne, Switzerland
Granger causality (GC) is, by design and purpose, not interested in this. It is a measure of causal effect, namely the reduction in prediction error when the causal interaction is taken into account, as compared to when it is ignored. [According to one version of neuroscience terminology (Friston, 2011), which attempts to draw a distinction between the different conceptions of connectivity, GC measures of causal effect yield directed “functional connectivity” maps when applied to neuroimaging data
Multiple properties of GC make it an elegant measure of causal effect. It satisfies crucial symmetry properties, including that GC from Y to X is invariant under rescalings of Y and X, as well as the addition of a multiple of X to Y, consistent with the measuring of independent predictive information about X contained in Y (Geweke, 1982; Hosoya, 1991; Barrett et al, 2010)

Summary

Introduction

Reviewed by: Marc-Oliver Gewaltig, Ecole Polytechnique Federale de Lausanne, Switzerland Athanassia Chalimourda, Ecole Polytechnique Federale de Lausanne, Switzerland. In their recent paper, Hu et al (2011) make the claim that Granger causality (GC) does not capture how strongly one time series influences another. Hu et al (2011) would like a measure of causal interaction to explicitly quantify an underlying causal mechanism, and point out that GC values do not consistently reflect the relative sizes of explicit interaction coefficients in a corresponding generative model.

Results

Conclusion