Telling cause from effect in deterministic linear dynamical systems

Telling a from its effect using observed time series data is a major challenge in natural and social sciences. Assuming the effect is generated by the through a linear system, we propose a new approach based on the hypothesis that nature chooses the and the mechanism generating the effect from the cause independently of each other. Specifically we postulate that the power spectrum of the time series is uncorrelated with the square of the frequency response of the linear filter (system) 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 exist even in deterministic systems. We describe mathematical assumptions in a deterministic model under which the causal direction is identifiable. In particular, we show a scenario where the method works but Granger causality fails. 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 observed time series.