title: Optimal model-free prediction from multivariate time series.
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 Niño Southern Oscillation.
authors.affiliation: Potsdam Institute for Climate Impact Research, P. O. Box 60 12 03, 14412 Potsdam, Germany.|Department of Physics, Humboldt University, Newtonstr. 15, 12489 Berlin, Germany.
authors.forename: Jakob
authors.initials: J
authors.lastname: Runge
authors.affiliation: Potsdam Institute for Climate Impact Research, P. O. Box 60 12 03, 14412 Potsdam, Germany.
authors.forename: Reik V
authors.initials: RV
authors.lastname: Donner
authors.affiliation: Potsdam Institute for Climate Impact Research, P. O. Box 60 12 03, 14412 Potsdam, Germany.|Department of Physics, Humboldt University, Newtonstr. 15, 12489 Berlin, Germany.|Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.|Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths
mesh_terms: D000465:Algorithms; D015982:Bias; D005544:Forecasting; D015999:Multivariate Analysis; D013997:Time Factors