Competitive online quantile regression

Interval prediction often provides more useful information compared to a simple point forecast. For example, in renewable energy forecasting, while the initial focus has been on deterministic predictions, the uncertainty observed in energy generation raises an interest in producing probabilistic forecasts. One aims to provide prediction intervals so that outcomes lie in the interval with a given probability. Therefore, the problem of estimating the quantiles of a variable arises. The contribution of our paper is two-fold. First, we propose to apply the framework of prediction with expert advice for the prediction of quantiles. Second, we propose a new competitive online algorithm Weak Aggregating Algorithm for Quantile Regression (WAAQR) and prove a theoretical bound on the cumulative loss of the proposed strategy. The theoretical bound ensures that WAAQR is asymptotically as good as any quantile regression. In addition, we provide an empirical survey where we apply both methods to the problem of probability forecasting of wind and solar powers and show that they provide good results compared to other predictive models.