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Conference Paper

#### Detecting the Direction of Causal Time Series

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##### Citation

Peters, J., Janzing, D., Gretton, A., & Schölkopf, B. (2009). Detecting the Direction
of Causal Time Series.* Proceedings of the 26th International Conference on Machine Learning (ICML
2009),* 801-808.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-C477-C

##### 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.