Time series: theory and methods
Time series: theory and methods
A Linear Non-Gaussian Acyclic Model for Causal Discovery
The Journal of Machine Learning Research
Measuring statistical dependence with hilbert-schmidt norms
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
Causal inference using the algorithmic Markov condition
IEEE Transactions on Information Theory
Gaussianity measures for detecting the direction of causal time series
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Learning Causal Relations in Multivariate Time Series Data
ACM Transactions on Intelligent Systems and Technology (TIST)
Statistical tests for the detection of the arrow of time in vector autoregressive models
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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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 identifiable). 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.