  We propose a novel tensor-based formalism for inferring causal structures
from time series. An information theoretical analysis of transfer entropy,
shows that transfer entropy results from transmission of information over a set
of communication channels. Tensors are the mathematical equivalents of these
multi-channel causal channels. A multi-channel causal channel is a
generalization of a discrete memoryless channel. Investigation of a system
comprising three variables shows that in our formalism, bivariate analysis
suffices to differentiate between direct and indirect relations. For this to be
true, we have to combine the output of multi-channel causal channels with the
output of single-channel causal channels. We can understand this result when we
consider the role of noise. Subsequent transmission of information over noisy
channels can never result in less noisy transmission overall. This implies that
a Data Processing Inequality exists for transfer entropy.
