  Transfer Entropy, a generalisation of Granger Causality, promises to measure
"information transfer" from a source to a target signal by ignoring
self-predictability of a target signal when quantifying the source-target
relationship. A simple example for signals with such self-predictability are
narrowband signals. These are both thought to be intrinsically generated by the
brain as well as commonly dealt with in analyses of brain signals, where
band-pass filters are used to separate responses from noise. However, the use
of Transfer Entropy is usually discouraged in such cases. We simulate
simplistic examples where we confirm the failure of classic implementations of
Transfer Entropy when applied to narrow-band signals, as made evident by a
flawed recovery of effect sizes and interaction delays. We propose an
alternative approach based on a whitening of the input signals before computing
a bivariate measure of directional time-lagged dependency. This approach solves
the problems found in the simple simulated systems. Finally, we explore the
behaviour of our measure when applied to delta and theta response components in
Magnetoencephalography (MEG) responses to continuous speech. The small effects
that our measure attributes to a directed interaction from the stimulus to the
neuronal responses are stronger in the theta than in the delta band. This
suggests that the delta band reflects a more predictive coupling, while the
theta band is stronger involved in bottom-up, reactive processing. Taken
together, we hope to increase the interest in directed perspectives on
frequency-specific dependencies.
