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Optimal model-free prediction from multivariate time series.

Jakob Runge1,2, Reik V Donner1, Jürgen Kurths1,2,3,4

  • 1Potsdam Institute for Climate Impact Research, P. O. Box 60 12 03, 14412 Potsdam, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2015
PubMed
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This study introduces a new causal preselection method for time series forecasting with many predictors. This approach efficiently identifies key drivers, making optimal model-free predictions computationally feasible.

Area of Science:

  • Time series analysis
  • Machine learning
  • Causal inference

Background:

  • Multivariate time series forecasting is challenging due to the curse of dimensionality and overfitting with model-free methods.
  • Existing techniques often limit applications to univariate cases, necessitating efficient predictor selection strategies.
  • Exhaustive subset testing is computationally prohibitive due to exponential growth in combinations.

Purpose of the Study:

  • To develop a computationally tractable method for optimal model-free multivariate time series forecasting.
  • To introduce a causal preselection step to drastically reduce the number of predictors.
  • To enable efficient variable selection and model fitting for improved predictions and statistical dependency learning.

Main Methods:

Related Experiment Videos

  • A novel prediction scheme utilizing a causal preselection step is introduced.
  • Information-theoretic optimality is derived for the selection criteria.
  • The framework is demonstrated on multivariate nonlinear stochastic delay processes and El Niño Southern Oscillation (ENSO) data.

    • Main Results:

    • The causal preselection method drastically reduces the predictor set to the most predictive causal drivers.
    • The optimal scheme is shown to be computationally less expensive than suboptimal methods like forward selection.
    • The framework effectively selects variables and fits models for improved prediction accuracy.

    Conclusions:

    • The proposed method overcomes the limitations of existing approaches for multivariate time series forecasting.
    • This causal preselection framework offers a general approach for optimal model-free variable selection and prediction.
    • The method's efficacy is validated through applications in complex stochastic processes and climatological forecasting.