Deeper relationship between Liang information flow rate and Wiener–Granger causality in linear systems

Determine whether a deeper formal relationship exists between Liang’s information flow rate and Wiener–Granger causality in linear systems, characterizing any equivalences, conditions for agreement, or mappings between the two frameworks.

Background

Wiener–Granger causality (WGC) is a classical, autoregressive-model-based approach to causality, while Liang’s information flow rate (IFR) derives from entropy and dynamical systems. Although transfer entropy and WGC are known to be equivalent under Gaussian assumptions, comparable formal results linking IFR and WGC have not been established.

The paper highlights the lack of systematic comparisons between IFR and WGC and explicitly states that, at least in the linear case, whether there is a deeper connection remains to be investigated. Resolving this would clarify how the two measures relate theoretically and guide their joint or alternative use in practice.