Gaussianity Measures for Detecting the Direction of Causal Time Series

Hernández-Lobato, José Miguel; Morales-Mombiela, Pablo; Suárez, Alberto

doi:10.5591/978-1-57735-516-8/IJCAI11-223

Gaussianity Measures for Detecting the Direction of Causal Time Series

José Miguel Hernández-Lobato, Pablo Morales-Mombiela, Alberto Suárez

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Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence. Pages 1318-1322.

https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-223

Abstract

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.

José Miguel Hernández-Lobato, Pablo Morales-Mombiela, and Alberto Suárez. 2011. Gaussianity Measures for Detecting the Direction of Causal Time Series. In Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI-11. IJCAI, 1318–1322. https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-223

@inproceedings{ijcai2011p223,
  title     = {Gaussianity Measures for Detecting the Direction of Causal Time Series},
  author    = {Hernández-Lobato, José Miguel and Morales-Mombiela, Pablo and Suárez, Alberto},
  booktitle = {Proceedings of the Twenty-Second International Joint Conference on
               Artificial Intelligence, {IJCAI-11}},
  publisher = {AAAI Press/International Joint Conferences on Artificial Intelligence},
  editor    = {Toby Walsh},
  pages     = {1318--1322},
  year      = {2011},
  month     = {7},
  doi       = {10.5591/978-1-57735-516-8/IJCAI11-223},
  url       = {https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-223},
}

TY  - CPAPER
TI  - Gaussianity Measures for Detecting the Direction of Causal Time Series
AU  - Hernández-Lobato, José Miguel
AU  - Morales-Mombiela, Pablo
AU  - Suárez, Alberto
T2  - Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI-11
PB  - AAAI Press/International Joint Conferences on Artificial Intelligence
PY  - 2011
SP  - 1318
EP  - 1322
DO  - 10.5591/978-1-57735-516-8/IJCAI11-223
UR  - https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-223
ER  -