Kernel Methods for Detecting the Direction of Time Series

  • Jonas Peters
  • Dominik Janzing
  • Arthur Gretton
  • Bernhard SchölkopfEmail author
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


We propose two kernel based methods for detecting the time direction in empirical time series. First we apply a Support Vector Machine on the finite-dimensional distributions of the time series (classification method) by embedding these distributions into a Reproducing Kernel Hilbert Space. For the ARMA method we fit the observed data with an autoregressive moving average process and test whether the regression residuals are statistically independent of the past values. Whenever the dependence in one direction is significantly weaker than in the other we infer the former to be the true one. Both approaches were able to detect the direction of the true generating model for simulated data sets. We also applied our tests to a large number of real world time series. The ARMA method made a decision for a significant fraction of them, in which it was mostly correct, while the classification method did not perform as well, but still exceeded chance level.


Classification Support vector machines Time series 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jonas Peters
  • Dominik Janzing
  • Arthur Gretton
  • Bernhard Schölkopf
    • 1
    Email author
  1. 1.MPI for biological CyberneticsTübingenGermany

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