Model selection and randomization for weakly dependent time series forecasting

Pierre Alquier (1, 2) , Olivier Wintenberger (3)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 CREST - Centre de Recherche en Économie et Statistique
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Observing a stationary time series, we propose in this pape new procedures in two steps for the prediction of the next value of the time series. Following machine learning theory paradigm, the first step consists in determining randomized estimators, or "experts", in (possibly numerous) different predictive models. In the second step estimators are obtained by model selection or randomization associated with exponential weights of these experts. We prove Oracle inequalities for both estimators and provide some applications for linear, artificial Neural Networks and additive non-parametric predictors.

Mots clés: Time series prediction; autoregression estimation; adaptative inference; statistical learning; randomized estimators; aggregation of estimators; model selection; weak dependence

Domaines: Méthodologie [stat.ME]; Statistiques [math.ST]

Pierre Alquier, Olivier Wintenberger. Model selection and randomization for weakly dependent time series forecasting. 2009. ⟨hal-00362151v1⟩