Detecting the Direction of causal Time Series
Jonas Peters, Dominik Janzing, Bernhard Schoelkopf, Arthur Gretton
(Max Plank Institute for Biological Cybernetics, Germany)
We propose a method to detect the time direction in empirical time series. The method infers cause and effect
and thereby detects the true time direction (every cause precedes its effect).
To this end, we fit the observed data with an auto-regressive moving average process (ARMA) and test whether the regression residuals are statistically independent of the past values. We prove that, for causal non-Gaussian ARMA processes with non-vanishing AR part, this can only be true for one time direction. Whenever the dependence in one direction is significantly weaker than in the other we infer the former to be the true one. This way, we were able to detect the direction of the true generating model for simulated data sets. We also applied our test to a large number of EEG time series and to a collection of time series. Our method made a decision for a significant fraction of them, in which it was mostly correct. Our result sheds light on the statistical asymmetries between cause and effect in empirical data.