# Comparison of Granger Causality and Phase Slope Index

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Guido Nolte,
Andreas Ziehe,
Nicole Krämer,
Florin Popescu,
Klaus-Robert Müller
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Proceedings of Workshop on Causality: Objectives and Assessment at NIPS 2008, PMLR 6:267-276, 2010.

#### Abstract

We recently proposed a new measure, termed Phase Slope Index (PSI), It estimates the causal direction of interactions robustly with respect to instantaneous mixtures of independent sources with arbitrary spectral content. We compared this method to Granger Causality for linear systems containing spatially and temporarily mixed noise and found that, in contrast to PSI, the latter was not able to properly distinguish truly interacting systems from mixed noise. Here, we extent this analysis with respect to two aspects: a) we analyze Granger causality and PSI also for non-mixed noise, and b) we analyze PSI for nonlinear interactions. We found a) that Granger causality, in contrast to PSI, fails also for non-mixed noise if the memory-time of the sender of information is long compared to the transmission time of the information, and b) that PSI, being a linear method, eventually misses nonlinear interactions but is unlikely to give false positive results.

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