Spectral causalities within dynamical effects framework

Spectral causalities are now widely used in physical and biological sciences to characterize directional couplings from time series. In particular, the Granger-Geweke spectrum is a frequency decomposition of a Wiener-Granger causality measure. However, there are considerable difficulties in their interpretation, so quite hot debates still arise. Here, the problem is studied within the dynamical effects framework: spectral effects are introduced as long-term effects of relevant parameter interventions. Quantitative relationships between the GG spectrum and certain spectral effects are established for linear stochastic differential equations. It is also argued that in general existing spectral causalities do not unambiguously relate to spectral effects. The latter are shown to be as estimable from time series, at least for some simple systems.