  Inferring a cause from its effect using observed time series data is a major
challenge in natural and social sciences. Assuming the effect is generated by
the cause trough a linear system, we propose a new approach based on the
hypothesis that nature chooses the "cause" and the "mechanism that generates
the effect from the cause" independent of each other. We therefore postulate
that the power spectrum of the time series being the cause is uncorrelated with
the square of the transfer function of the linear filter generating the effect.
While most causal discovery methods for time series mainly rely on the noise,
our method relies on asymmetries of the power spectral density properties that
can be exploited even in the context of deterministic systems. We describe
mathematical assumptions in a deterministic model under which the causal
direction is identifiable with this approach. We also discuss the method's
performance under the additive noise model and its relationship to Granger
causality. Experiments show encouraging results on synthetic as well as
real-world data. Overall, this suggests that the postulate of Independence of
Cause and Mechanism is a promising principle for causal inference on empirical
time series.
