Optimal model-free prediction from multivariate time series

Jakob Runge, Reik V. Donner, Juergen Kurths

Research output: Contribution to journalArticle

16 Citations (Scopus)
5 Downloads (Pure)

Abstract

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
Volume91
Issue number5
DOIs
Publication statusPublished - 13 May 2015

Keywords

  • El-Nino

Cite this

Optimal model-free prediction from multivariate time series. / Runge, Jakob; Donner, Reik V.; Kurths, Juergen.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 91, No. 5, 052909, 13.05.2015.

Research output: Contribution to journalArticle

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