Validation of the hidden harmonic methodology. Four different model configurations are considered. In each configuration node X has a causal influence of node Y. In (i) both of the nodes have environmental inputs, in (ii) and (iii) the simulation has just node X or node Y have an external input, in (iv) neither X or Y have external inputs. (A) shows the connection configurations. In (B) and (C) the power spectra of each configuration are shown in frequency domain, node X is shown in blue, node Y is shown in green. (D) and (E) show the causality spectra from X to Y, fX→Y, the causality calculated using the normal Granger AR method is shown in column (D), the harmonic causal method is shown in column (E).