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 efficient modeling 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 (absolute shrinkage and selection operator), 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 using historical data from the German day-ahead market, the proposed method yields interpretable and well-calibrated joint prediction intervals for the 24-dimensional price distribution and provides robust performance across a range of proper scoring rules. The results underscore the importance of modeling the dependence structure of electricity prices. Furthermore, we analyze the trade-off between predictive accuracy and computational costs for batch and online estimation and provide a high-performing open-source Python implementation in the ondil package.

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