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Detecting the Direction of Causal Time Series

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons84134

Peters,  J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons75626

Janzing,  D
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83946

Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

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.


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