Information Flow — Transfer Entropy & Granger Causality

Directed information · TE(X→Y) · bivariate coupling detection

Coupling X→Y (c_xy) 0.40

Coupling Y→X (c_yx) 0.10

Noise level σ 0.30

Autocorr. ρ 0.60

Transfer Entropy

TE(X→Y)—

TE(Y→X)—

Net flow—

Granger Causality

GC(X→Y)—

GC(Y→X)—

Dominant—

Transfer entropy TE(X→Y) = Σ p(y_{t+1},y_t,x_t) log[p(y_{t+1}|y_t,x_t)/p(y_{t+1}|y_t)] measures directional information flow from X to Y beyond Y's own history. Granger causality tests whether X's past helps predict Y's future. Both detect asymmetric coupling in coupled stochastic systems. Here X and Y are coupled AR(1) processes.