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

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Title: Prediction of time series by statistical learning: general losses and fast rates
Authors: Alquier, Pierre
Li, Xiaoyin
Wintenberger, Olivier
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Date: 31-Dec-2013
Abstract: 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.
Type of material: Journal Article
Publisher: De Gruyter
Journal: Dependence Modelling
Volume: 1
Start page: 65
End page: 93
Copyright (published version): 2013 the Authors
Keywords: Recommender systemsStatistical learning theoryTime series forecastingPAC-Bayesian boundsWeak dependenceMixingOracle inequalitiesFast ratesGDP forecasting
DOI: 10.2478/demo-2013-0004
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection
Insight Research Collection

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