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

Runyao Yu^1,2, Yuchen Tao³, Fabian Leimgruber², Tara Esterl², Jochen Stiasny¹,

Qingsong Wen⁴, Hongye Guo⁵, Jochen L. Cremer^1,2

¹ Delft University of Technology, ² Austrian Institute of Technology,
³ RWTH Aachen, ⁴ Squirrel Ai Learning, ⁵ Tsinghua University
Preprint

Code Paper

Example forecasting on testing samples

Abstract

Probabilistic forecasting of intraday electricity prices is essential to manage market uncertainties. We propose an end-to-end forecasting model called OrderFusion. The backbone encodes the orderbook into a 2.5D representation and employs fusion layers to form rich representations of buy-sell interactions, avoiding handcrafted feature extraction and enabling parameter-efficient learning. The prediction head hierarchically estimates multiple quantiles through constrained residuals, eliminating the need to train separate models and overcoming quantile crossing. We conduct extensive experiments and ablation studies on widely used price indices (ID1, ID2, and ID3) using three years of orderbook in high-liquidity (German) and low-liquidity (Austrian) markets. The results confirm that OrderFusion remains end-to-end, parameter-efficient, and generalizable across different markets.

Structure of OrderFusion. Buy and sell inputs are iteratively fused to form the high-level representation of buy-sell interactions, which is then processed by the prediction head to generate quantile estimates, enabling end-to-end probabilistic forecasting.

Visualization of buy-sell interactions for electricity delivery at 18:00 on 2024-07-23. Each circle represents a trade, with color indicating the side (buy or sell) and size proportional to the traded volume. Buyers adjust their bids based on information observed from sellers, while sellers respond based on bids submitted by buyers, reflecting strategic interactions. As the delivery time approaches, prices exhibit a downward trend, suggesting intensified buy-sell interactions.

Visualization of price indices in the German market (2024). Each subfigure shows the 3D distribution of prices over time and hour of day. The second half of 2024 illustrates significant extreme price spikes, indicating challenging forecasting tasks. Overall, volatility follows the order: ID1 > ID2 > ID3. a ID1 displays frequent price spikes, reflecting last-minute trading under imbalance pressure. b ID2 reflects mid-session adjustments with slightly lower volatility. c ID3 corresponds to the most liquid trading window, exhibiting the least volatility and price spikes.

Results in the German market.

Results in the Austrian market.

BibTeX

If you use our code or find our paper useful, please cite:

@misc{yu2025orderfusion,
      title={OrderFusion: Encoding Orderbook for End-to-End Probabilistic Intraday Electricity Price Forecasting}, 
      author={Runyao Yu and Yuchen Tao and Fabian Leimgruber and Tara Esterl and Jochen Stiasny and Qingsong Wen and Hongye Guo and Jochen L. Cremer},
      year={2025},
      eprint={2502.06830},
      archivePrefix={arXiv},
      primaryClass={q-fin.CP},
      url={https://arxiv.org/abs/2502.06830}, 
}