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Model selection for weakly dependent time series forecasting

Alquier, Pierre; Wintenberger, Olivier (2012), Model selection for weakly dependent time series forecasting, Bernoulli, 18, 3, p. 883-913. http://dx.doi.org/10.3150/11-BEJ359

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00362151
Date
2012
Journal name
Bernoulli
Volume
18
Number
3
Publisher
Bernoulli Society for Mathematical Statistics and Probability
Pages
883-913
Publication identifier
http://dx.doi.org/10.3150/11-BEJ359
Metadata
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Author(s)
Alquier, Pierre
Wintenberger, Olivier
Abstract (EN)
Observing a stationary time series, we propose a two-steps procedure for the prediction of its next value. The first step follows machine learning theory paradigm and consists in determining a set of possible predictors as randomized estimators in (possibly numerous) different predictive models. The second step follows the model selection paradigm and consists in choosing one predictor with good properties among all the predictors of the first step. We study our procedure for two different types of observations: causal Bernoulli shifts and bounded weakly dependent processes. In both cases, we give oracle inequalities: the risk of the chosen predictor is close to the best prediction risk in all predictive models that we consider. We apply our procedure for predictive models as linear predictors, neural networks predictors and nonparametric autoregressive predictors.
Subjects / Keywords
adaptative inference; aggregation of estimators; autoregression estimation; model selection; randomized estimators; statistical learning; time series prediction; weak dependence

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