Time series: theory and methods
Time series: theory and methods
A Hilbert Space Embedding for Distributions
ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
Detecting the direction of causal time series
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Causality Discovery with Additive Disturbances: An Information-Theoretical Perspective
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part II
Hilbert Space Embeddings and Metrics on Probability Measures
The Journal of Machine Learning Research
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 conjecture that the distribution of the time-reversed residuals of a causal linear process is closer to a Gaussian than the distribution of the noise used to generate the process in the forward direction. This property is demonstrated for causal AR(1) processes assuming that all the cumulants of the distribution of the noise are defined. Based on this observation, it is possible to design a decision rule for detecting the direction of time series that can be described as linear processes: The correct direction (forward in time) is the one in which the residuals from a linear fit to the time series are less Gaussian. A series of experiments with simulated and real-world data illustrate the superior results of the proposed rule when compared with other state-of-the-art methods based on independence tests.