Electricity price forecasting approaches generally fall into two categories: data-driven models, which learn from historical patterns, or fundamental models, which simulate market mechanisms. We propose a novel and highly efficient data-driven merit order model that integrates both paradigms. The resulting supply stack framework embeds the classical expert-based merit order as a nested special case, allowing all key parameters, such as plant efficiencies, bidding behavior, and available capacities, to be estimated directly from historical data, rather than assumed. We further enhance the model with critical embedded extensions such as hydro power, cross-border flows and corrections for underreported capacities, which considerably improve forecasting accuracy. Applied to the German day-ahead market, our model outperforms both classic fundamental and state-of-the-art machine learning models. It retains the interpretability of fundamental models, offering insights into marginal technologies, fuel switches, and dispatch patterns, elements which are typically inaccessible to black-box machine learning approaches. This transparency and high computational efficiency make it a promising new direction for electricity price modeling.

This paper presents a new method for combining (or aggregating or ensembling) multivariate probabilistic forecasts, considering dependencies between quantiles and marginals through a smoothing procedure that allows for online learning. We discuss two smoothing methods: dimensionality reduction using Basis matrices and penalized smoothing. The new online learning algorithm generalizes the standard CRPS learning framework into multivariate dimensions. It is based on Bernstein Online Aggregation (BOA) and yields optimal asymptotic learning properties. The procedure uses horizontal aggregation, i.e., aggregation across quantiles. We provide an in-depth discussion on possible extensions of the algorithm and several nested cases related to the existing literature on online forecast combination. We apply the proposed methodology to forecasting day-ahead electricity prices, which are 24-dimensional distributional forecasts. The proposed method yields significant improvements over uniform combination in terms of continuous ranked probability score (CRPS). We discuss the temporal evolution of the weights and hyperparameters and present the results of reduced versions of the preferred model. A fast C＋＋implementation of the proposed algorithm is provided in the open-source R-Package profoc on CRAN.

Combination and aggregation techniques can significantly improve forecast accuracy. This also holds for probabilistic forecasting methods where predictive distributions are combined. There are several time-varying and adaptive weighting schemes such as Bayesian model averaging (BMA). However, the quality of different forecasts may vary not only over time but also within the distribution. For example, some distribution forecasts may be more accurate in the center of the distributions, while others are better at predicting the tails. Therefore, we introduce a new weighting method that considers the differences in performance over time and within the distribution. We discuss pointwise combination algorithms based on aggregation across quantiles that optimize with respect to the continuous ranked probability score (CRPS). After analyzing the theoretical properties of pointwise CRPS learning, we discuss B- and P-Spline-based estimation techniques for batch and online learning, based on quantile regression and prediction with expert advice. We prove that the proposed fully adaptive Bernstein online aggregation (BOA) method for pointwise CRPS online learning has optimal convergence properties. They are confirmed in simulations and a probabilistic forecasting study for European emission allowance (EUA) prices.