Rendering statistical significance of information flow measures

Information causality measures, i.e. transfer entropy and symbolic transfer entropy, are modified using the concept of surrogate data in order to identify correctly the presence and direction of causal effects. The measures are evaluated on multiple bivariate time series of known coupled systems of varying complexity and on a range of embedding dimensions. The proposed modifications of the causality measures are found to reduce the bias in the estimation of the measures and preserve the zero level in the absence of coupling.