Time Series Causality Inference Using the Phase Slope Index

A method recently introduced by Nolte et. al (Phys Rev Lett 100:23401, 2008) estimates the causal direction of interactions robustly with respect to instantaneous mixtures of independent sources with arbitrary spectral content, i.e. in observations which are dominated by non-white spatially correlated noise and in which dynamic structural interaction plays little part. The method, named Phase Slope Index (PSI), is unlikely to assign causality in the case of lack of dynamic interaction among time series, unlike Granger causality for linear systems. Results show that PSI does not yield false positives even in the case of nonlinear interactions. The meaning of instaneous noise mixtures in different data domains will be discussed in the context of correct correlation vs. causation inference, and the theoretical relationship of PSI to other time-series causality inference methods will be expanded upon.