Day-ahead probabilistic forecasting for French half-hourly electricity loads and quantiles for curve-to-curve regression

The probabilistic forecasting of electricity loads is crucial for effective scheduling and decision-making in volatile and competitive energy markets with ever-growing uncertainties. We propose a novel approach to construct the probabilistic predictors for curves (PPC) of electricity loads, which leads to properly defined predictive bands and quantiles in the context of curve-to-curve regression. The proposed predictive model provides not only accurate hourly load point forecasts, but also generates well-defined probabilistic bands and day-long trajectories of the loads at any probability level, pre-specified by managers. We also define the predictive quantile curves that exhibit future loads in extreme scenarios and provide insights for hedging risks in the supply management of electricity. When applied to the day-ahead forecasting for French half-hourly electricity loads, the PPC outperform several state-of-the-art time series and machine learning predictive methods with more accurate point forecasts (mean absolute percentage error of 1.10%, compared to 1.36%–4.88% for the alternatives), a higher coverage rate of the day-long trajectory of loads (coverage rate of 95.5%, against 31.9%–90.7% for the alternatives) and a narrower average length of the predictive bands. In a series of numerical experiments, the PPC further demonstrate robust performance and general applicability, achieving accurate coverage probabilities under a variety of data-generating mechanisms.