Abstract
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.
Highlights
After 25 years of intensive research, the electricity price forecasting (EPF) literature includes hundreds of publications, focused both on point [1,2] and probabilistic [3,4] predictions
The difference between them lies in the choice of the regressors—Quantile Regression Averaging (QRA) uses the point forecasts themselves, while Quantile Regression Machine (QRM) first averages them, applies quantile regression to the combined forecast
That Equation (8) measures the predictive accuracy for only one particular quantile. It can be averaged across all percentiles (i.e., q = 0.01, 0.02, ..., 0.99) and all hours in the whole out-of-sample test period to yield the Aggregate Pinball Score (APS)
Summary
After 25 years of intensive research, the electricity price forecasting (EPF) literature includes hundreds of publications, focused both on point [1,2] and probabilistic [3,4] predictions. Using data from the Global Energy Forecasting Competition 2014, they showed that such averaging across calibration windows yielded better results than selecting ex-ante only one ‘optimal’ window length. They concluded that a mix of a few short- and a few long-term windows led to the best predictions. Marcjasz et al [6] extended their analysis to other datasets and larger models They introduced a well-performing weighting scheme for averaging forecasts. Overall, their results confirmed earlier findings, but they advised to use slightly longer windows at the shorter end, especially when considering models with more explanatory variables (inputs). Marcjasz et al recommended the WAW(56:28:112, 714:7:728) averaging scheme, i.e., past performance weighted combination of forecasts
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