Kernel Methods for Detecting the Direction of Time Series

2010

Conference Paper

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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.

Author(s): Peters, J. and Janzing, D. and Gretton, A. and Schölkopf, B.
Book Title: Advances in Data Analysis, Data Handling and Business Intelligence
Journal: Advances in Data Analysis, Data Handling and Business Intelligence
Pages: 57-66
Year: 2010
Day: 0
Editors: A Fink and B Lausen and W Seidel and A Ultsch
Publisher: Springer

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Address: Berlin, Germany
Digital: 0
DOI: 10.1007/978-3-642-01044-6_5
Event Name: 32nd Annual Conference of the Gesellschaft f{\"u}r Klassifikation e.V. (GfKl 2008)
Event Place: Hamburg, Germany
Institution: Gesellschaft für Klassifikation
ISBN: 978-3-642-01044-6
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{5662,
  title = {Kernel Methods for Detecting the Direction of Time Series },
  author = {Peters, J. and Janzing, D. and Gretton, A. and Sch{\"o}lkopf, B.},
  journal = {Advances in Data Analysis, Data Handling and Business Intelligence},
  booktitle = {Advances in Data Analysis, Data Handling and Business Intelligence},
  pages = {57-66},
  editors = {A Fink and B Lausen and W Seidel and A Ultsch},
  publisher = {Springer},
  organization = {Max-Planck-Gesellschaft},
  institution = {Gesellschaft für Klassifikation},
  school = {Biologische Kybernetik},
  address = {Berlin, Germany},
  year = {2010}
}