Averaging predictive distributions across calibration windows for day-ahead electricity price forecasting

The recent developments in combining point forecasts of day-ahead electricity prices across calibration windows have provided an extremely simple, yet a very efficient tool for improving predictive accuracy. Here, we consider two novel extensions of this concept to probabilistic forecasting: one based on Quantile Regression Averaging (QRA) applied to a set of point forecasts obtained for different calibration windows, the other on a technique dubbed Quantile Regression Machine (QRM), which first averages these point predictions, then applies quantile regression to the combined forecast. Once computed, we combine the probabilistic forecasts across calibration windows by averaging probabilities of the corresponding predictive distributions. Our results show that QRM is not only computationally more efficient, but also yields significantly more accurate distributional predictions, as measured by the aggregate pinball score and the test of conditional predictive ability. Moreover, combining probabilistic forecasts brings further significant accuracy gains.