On causality and mutual information

We provide for the first time a formulation of non-linear, nonstationary causality in terms of mutual information. We provide two fundamental mutual information identities; the first relating Granger type causality to Sims type causality. The second providing a decomposition of mutual information into a sum of Granger and Sims type terms. We also develop asymptotic relations that emerge under strict stationarity and generalise earlier work of Geweke. We relate our work in general with earlier developments.