@inproceedings{5902,
  title = {Detecting the Direction of Causal Time Series},
  booktitle = {Proceedings of the 26th International Conference on Machine Learning},
  abstract = {We propose a method that detects the true
  direction of time series, by fitting an autoregressive
  moving average model to the data.
  Whenever the noise is independent of the previous
  samples for one ordering of the observations,
  but dependent for the opposite ordering,
  we infer the former direction to be the
  true one. We prove that our method works
  in the population case as long as the noise of
  the process is not normally distributed (for
  the latter case, the direction is not identificable).
  A new and important implication of
  our result is that it confirms a fundamental
  conjecture in causal reasoning - if after regression
  the noise is independent of signal for
  one direction and dependent for the other,
  then the former represents the true causal
  direction - in the case of time series. We
  test our approach on two types of data: simulated
  data sets conforming to our modeling
  assumptions, and real world EEG time series.
  Our method makes a decision for a significant
  fraction of both data sets, and these
  decisions are mostly correct. For real world
  data, our approach outperforms alternative
  solutions to the problem of time direction recovery.},
  pages = {801-808},
  editors = {A Danyluk and L Bottou and ML Littman},
  publisher = {ACM Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {New York, NY, USA},
  month = jun,
  year = {2009},
  slug = {5902},
  author = {Peters, J. and Janzing, D. and Gretton, A. and Sch{\"o}lkopf, B.},
  month_numeric = {6}
}