Optimal model-free prediction from multivariate time series

Jakob Runge*, Reik V. Donner, Juergen Kurths

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)
8 Downloads (Pure)


Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal preselection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used suboptimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Nino Southern Oscillation.

Original languageEnglish
Article number052909
Number of pages14
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number5
Publication statusPublished - 13 May 2015

Bibliographical note

We acknowledge the financial support by the German National Merit Foundation (Studienstiftung des deutschen Volkes), the Humboldt Graduate School, and the German Federal Ministry of Education and Research (Young Investigators Group CoSy-CC2, Grant No. 01LN1306A).


  • El-Nino


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