Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting

Probabilistic electricity price forecasting (PEPF) is vital for short-term electricity markets, yet the multivariate nature of day-ahead prices - spanning 24 consecutive hours - remains underexplored. At the same time, real-time decision-making requires methods that are both accurate and fast. We introduce an online algorithm for multivariate distributional regression models, allowing an efficient modelling of the conditional means, variances, and dependence structures of electricity prices. The approach combines multivariate distributional regression with online coordinate descent and LASSO-type regularization, enabling scalable estimation in high-dimensional covariate spaces. Additionally, we propose a regularized estimation path over increasingly complex dependence structures, allowing for early stopping and avoiding overfitting. In a case study of the German day-ahead market, our method outperforms a wide range of benchmarks, showing that modeling dependence improves both calibration and predictive accuracy. Furthermore, we analyse the trade-off between predictive accuracy and computational costs for batch and online estimation and provide an high-performing open-source Python implementation in the ondil package.