OrderFusion: Encoding Orderbook for End-to-End Probabilistic Intraday Electricity Price Prediction

Accurate and reliable probabilistic prediction of intraday electricity prices is essential to manage market uncertainties and support robust trading strategies. However, current methods rely heavily on domain feature extraction and fail to capture the dynamics between buy and sell orders, limiting the ability to form rich representations of the orderbook. Furthermore, these methods often require training separate models for different quantiles and introduce additional procedures-such as post-hoc quantile sorting or loss-based penalties-to address the quantile crossing issue, where predicted upper quantiles fall below lower ones. These steps are either decoupled from model training or introduce extra tuning complexity. To address these challenges, we propose an encoding method called OrderFusion and design a hierarchical multi-quantile head. OrderFusion encodes the orderbook into a 2.5D representation and employs a tailored jump cross-attention to model buy-sell dynamics without the need for domain feature extraction. The multi-quantile head anchors on the median quantile and hierarchically estimates other quantiles through constrained residuals, ensuring monotonicity without post-processing or additional tuning. We conduct extensive experiments and ablation studies on three key price indices (ID1, ID2, and ID3) using three years of orderbook data from the German and Austrian markets. The results demonstrate that our approach provides an accurate, reliable, and unified end-to-end framework for probabilistic intraday price prediction.