Comparison of Granger Causality and Phase Slope Index
Guido Nolte, Andreas Ziehe, Nicole Krämer, Florin Poupescu and Klaus-Robert Müller
In: NIPS08 workshop on Causality, 12 Dec 2008, Whistler, Canada.
We recently proposed a new measure, termed Phase Slope Index (PSI), to estimate the causal direction of interactions designed to be robust 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.