Fast asymptotic algorithm for real-time causal connectivity analysis of multivariate systems and signals

•A fast asymptotic algorithm for statistical assessment of the connectivity Granger-causality measures in the frequency domain is introduced•The real-time derivation of asymptotic statistics of the Directed Transfer Function (DTF), Partial Directed Coherence (PDC), and their variants in high-dimensional time series is feasible•The fast asymptotic algorithm runs at least three orders of magnitude faster than the current state-of-the-art asymptotic algorithm•The fast asymptotic algorithm (FAA) is made publicly available on GitHub.