64,640 research outputs found
A comparative evaluation of nonlinear dynamics methods for time series prediction
A key problem in time series prediction using autoregressive models is to fix the model order, namely the number of past samples required to model the time series adequately. The estimation of the model order using cross-validation may be a long process. In this paper, we investigate alternative methods to cross-validation, based on nonlinear dynamics methods, namely Grassberger-Procaccia, K,gl, Levina-Bickel and False Nearest Neighbors algorithms. The experiments have been performed in two different ways. In the first case, the model order has been used to carry out the prediction, performed by a SVM for regression on three real data time series showing that nonlinear dynamics methods have performances very close to the cross-validation ones. In the second case, we have tested the accuracy of nonlinear dynamics methods in predicting the known model order of synthetic time series. In this case, most of the methods have yielded a correct estimate and when the estimate was not correct, the value was very close to the real one
Optimal model-free prediction from multivariate time series
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 pre-selection 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 sub-optimal 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 Ni\~no Southern Oscillation.Comment: 14 pages, 9 figure
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