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Centre de Recherche en Économie et Statistique |  |
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Centre de Recherche en Économie et Statistique | |
| HAL: hal-00362151, version 4 |
| arXiv: 0902.2924 |
| DOI: 10.3150/11-BEJ359 |
| Detailed view |  Export this paper |
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| Bernoulli 18, 3 (2012) pp 883-913 |
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| Available versions: | v1 (2009-02-17) | v2 (2009-02-25) | v3 (2010-09-06) | v4 (2012-07-03) |
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| Model selection for weakly dependent time series forecasting |
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| Pierre Alquier 1, 2Olivier Wintenberger 3 |
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| (2012-08-01) |
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| Observing a stationary time series, we propose a two-step procedure for the prediction of the next value of the time series. 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 steps. We study our procedure for two different types of bservations: 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 such as linear predictors, neural networks predictors and non-parametric autoregressive. |
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| 1: | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot |
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| 2: | Centre de Recherche en Économie et Statistique (CREST) |
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INSEE – École Nationale de la Statistique et de l'Administration Économique |
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| 3: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| Subject | : | Statistics/Methodology Mathematics/Statistics Statistics/Statistics Theory |
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| Time series prediction – autoregression estimation – adaptative inference – statistical learning – randomized estimators – aggregation of estimators – model selection – weak dependence |
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| hal-00362151, version 4 | |
| http://hal.archives-ouvertes.fr/hal-00362151 | |
| oai:hal.archives-ouvertes.fr:hal-00362151 | |
| From: Pierre Alquier | |
| Submitted on: Tuesday, 3 July 2012 10:03:50 | |
| Updated on: Tuesday, 3 July 2012 17:02:08 | |
