(A) Scalar time courses of processes

coupled

with delay

, as indicated by the blue arrow. Colored boxes with circles indicate data belonging to a certain state of the respective process. The star on the

time series indicates the scalar observation

to be predicted in Wiener’s sense. Three settings for the delay parameter

are depicted: (1)

with – u is chosen such that influences of the state

on

arrive in the future of the prediction point. Hence, the information in this state is useless and yields no transfer entropy. (2)

– u is chosen such that influences of the state

arrive exactly at the prediction point, and influence it. Information about this state is useful, and we obtain nonzero transfer entropy. (3)

– u is chosen such that influences of the state

arrive in the far past of prediction point. This information is already available in the past of the states of

that we condition upon in

Information about this state is useless again, and we obtain zero transfer entropy. (B) Depiction of the same idea in a more detailed view, depicting states (gray boxes) of

and the samples of the most informative state (black circles) and noninformative states (white circles). The the curve in the left column indicates the approximate dependency of

versus

. The red circles indicates the value obtained with the respectzive states on the right.

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