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Prediction of quantiles by statistical learning and application to GDP forecasting
Pierre Alquier1, 2, Xiaoyin Li3

In this paper, we tackle the problem of prediction and confidence intervals for time series using a statistical learning approach and quantile loss functions. In a first time, we show that the Gibbs estimator (also known as Exponentially Weighted aggregate) is able to predict as well as the best predictor in a given family for a wide set of loss functions. In particular, using the quantile loss function of Koenker and Bassett (1978), this allows to build confidence intervals. We apply these results to the problem of prediction and confidence regions for the French Gross Domestic Product (GDP) growth, with promising results.
1 :  LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 :  CREST - Centre de Recherche en Économie et Statistique
3 :  AGM - Laboratoire d'Analyse, Géométrie et Modélisation
Statistical learning theory – Time series prediction – Quantile regression – GDP forecasting – PAC-Bayesian bounds – Oracle inequalities – Weak dependence – Confidence intervals – Business surveys