OrderFusion: Encoding Orderbook for Probabilistic Intraday Price Prediction

Efficient and reliable probabilistic prediction of intraday electricity prices is essential to manage market uncertainties and support robust trading strategies. However, current methods often suffer from parameter inefficiencies, as they fail to fully exploit the potential of modeling interdependencies between bids and offers in the orderbook, requiring a large number of parameters for representation learning. Furthermore, these methods face the quantile crossing issue, where upper quantiles fall below the lower quantiles, resulting in unreliable probabilistic predictions. To address these two challenges, we propose an encoding method called OrderFusion and design a hierarchical multi-quantile head. The OrderFusion encodes the orderbook into a 2.5D representation, which is processed by a tailored jump cross-attention backbone to capture the interdependencies of bids and offers, enabling parameter-efficient learning. The head sets the median quantile as an anchor and predicts multiple quantiles hierarchically, ensuring reliability by enforcing monotonicity between quantiles through non-negative functions. Extensive experiments and ablation studies are conducted on four price indices: 60-min ID3, 60-min ID1, 15-min ID3, and 15-min ID1 using the German orderbook over three years to ensure a fair evaluation. The results confirm that our design choices improve overall performance, offering a parameter-efficient and reliable solution for probabilistic intraday price prediction.