Causal graph for two coupled systems .

Illustration of d-separation of and by . Arrows indicate a causal influence (directed interaction). Solid lines indicate a single time step, broken lines an arbitrary number of time steps. The black circle is the state to be predicted in Wiener’s sense, the red circles indicate the states that form its set of parents in the graphs. These states are also the ones conditioned upon in the novel estimator . The blue circle indicates the state in the graph for which we want to determine that forms a Markov chain: . For all sequential paths from into are blocked, as are the divergent paths between these nodes. All convergent paths (e.g. via in (B)) are not blocked. This holds for (A) and (B).