Inadequacy of the Liang Information Flow for Causal Analysis

The Liang information flow is a measure of causality between components of d-dimensional observed time series X. The power of the approach was recently presented on an example of a realization of two unidirectly coupled chaotic Rössler systems. Different from Liang’s publication, where a causal inference involved only the magnitude of the information flow estimates, here, statistical significance is tested, and the properties of the estimators are analysed. It is demonstrated that the approach is not efficient for application in non-linear deterministic systems in general. Instead of correctly detecting a unidirectional connection, the bidirectional connection was statistically detected between analysed variables.