Transfer entropy

Transfer entropy is an information-theoretic measure of directed information flow from one time series to another, introduced by Thomas Schreiber in 2000. Unlike mutual information, which is symmetric and captures undirected statistical dependence, transfer entropy is asymmetric: it quantifies how much knowing the past of one process reduces uncertainty about the present of another, beyond what is already explained by the target's own history. In this sense, it attempts to capture "Granger causality" in information-theoretic terms.\n\nTransfer entropy has been widely applied in neuroscience (to map information flow between brain regions), climatology (to identify ocean-atmosphere couplings), and finance (to detect lead-lag relationships between markets). Its limitation is that it detects predictive relationships, not necessarily causal ones: a variable may have high transfer entropy toward another simply because both are driven by a common unobserved cause. The measure also struggles with non-stationary systems, where the statistical relationships change over time.\n\nSee also: Mutual information, Granger causality, Complex systems theory, Information theory, Causal inference\n\n