Prediction of quantiles by statistical learning and application to GDP forecasting

TL;DR

This paper introduces a statistical learning method using the Gibbs estimator and quantile loss functions to improve time series prediction and confidence intervals, demonstrated on French GDP growth forecasting.

Contribution

It demonstrates that the Gibbs estimator can effectively predict and construct confidence intervals for time series using quantile loss functions, with practical application to GDP forecasting.

Findings

Gibbs estimator performs comparably to the best predictors in a family.

Quantile loss functions enable accurate confidence interval construction.

Application to French GDP shows promising results.

Abstract

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.