Prediction of time series by statistical learning: general losses and fast rates

• Autorzy: Pierre Alquier , Xiaoyin Li , Olivier Wintenberger
• Języki publikacji: EN

Abstrakty

EN

We establish rates of convergences in statistical learning for time series forecasting. Using the PAC-Bayesian approach, slow rates of convergence √ d/n for the Gibbs estimator under the absolute loss were given in a previous work [7], where n is the sample size and d the dimension of the set of predictors. Under the same weak dependence conditions, we extend this result to any convex Lipschitz loss function. We also identify a condition on the parameter space that ensures similar rates for the classical penalized ERM procedure. We apply this method for quantile forecasting of the French GDP. Under additional conditions on the loss functions (satisfied by the quadratic loss function) and for uniformly mixing processes, we prove that the Gibbs estimator actually achieves fast rates of convergence d/n. We discuss the optimality of these different rates pointing out references to lower bounds when they are available. In particular, these results bring a generalization the results of [29] on sparse regression estimation to some autoregression.

Słowa kluczowe

EN

Statistical learning theory; time series forecasting; PACBayesian bounds; weak dependence; mixing; oracle inequalities; fast rates; GDP forecasting

Kategorie tematyczne

• 60G25: Prediction theory
• 68Q32: Computational learning theory
• 68T05: Learning and adaptive systems
• 62M10: Time series, auto-correlation, regression, etc.
• 62P20: Applications to economics
• 62M20: Prediction

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2013
• Tom: 1
• Strony: 65-93

Daty

otrzymano

2013-10-23

zaakceptowano

2013-12-08

online

2013-12-31

Twórcy

autor

Pierre Alquier

• University College Dublin, School of Mathematical Sciences
• INSIGHT Centre for Data Analytics

autor

Xiaoyin Li

• Université de Cergy, Laboratoire Analyse Géométrie Modélisation

autor

Olivier Wintenberger

• Université Paris-Dauphine, CEREMADE
• ENSAE, CREST

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Identyfikatory

DOI

10.2478/demo-2013-0004