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

This paper introduces OrderFusion, an end-to-end, parameter-efficient probabilistic forecasting model that utilizes a novel order fusion methodology to capture the full interaction structure of continuous intraday electricity orderbooks, thereby outperforming conventional baselines in predicting prices across varying market liquidity conditions while ensuring non-crossing quantile estimates.

Original authors: Runyao Yu, Yuchen Tao, Fabian Leimgruber, Tara Esterl, Jochen Stiasny, Derek W. Bunn, Qingsong Wen, Hongye Guo, Jochen L. Cremer

Published 2026-05-12

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Runyao Yu, Yuchen Tao, Fabian Leimgruber, Tara Esterl, Jochen Stiasny, Derek W. Bunn, Qingsong Wen, Hongye Guo, Jochen L. Cremer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Predicting the Next Price of Electricity

Imagine the electricity market not as a giant factory, but as a bustling online auction house that never sleeps. Unlike the "Day-Ahead" market, which is like a scheduled auction where everyone bids once a day, the Continuous Intraday (CID) market is like a live, chaotic stock exchange. Buyers and sellers are constantly shouting out new prices and quantities, trying to adjust their positions right up until the moment the electricity is actually delivered.

The goal of this paper is to build a "crystal ball" that can predict what the price of electricity will be in the next few hours. But instead of just guessing a single number (e.g., "It will be $50"), the authors want to predict a range of possibilities (e.g., "It's likely between $45 and $55, but could spike to $80"). This is called probabilistic forecasting, and it helps power companies manage risk.

The Problem: The Old Way Was Too Simple

Previously, people tried to predict these prices by looking at the "orderbook" (the list of all buy and sell orders) in two main ways, both of which had flaws:

The "Summary Sheet" Approach (1D Encoding): Imagine trying to understand a complex conversation between two people by only reading a summary of what they said. Old methods took the buy orders and sell orders, mashed them together, and calculated simple averages (like the average price of the last 15 minutes).
- The Flaw: This ignores the conversation. It misses the fact that a buyer might raise their bid because they saw a seller lower their price. It treats the market as a static list rather than a dynamic interaction.
The "Heavy Machine" Approach (2D Encoding): Other researchers tried to feed the raw list of orders into massive, complex AI models (like advanced Transformers).
- The Flaw: These models are like using a sledgehammer to crack a nut. They are huge, require a lot of computing power, and because they don't "know" how buyers and sellers interact, they have to learn everything from scratch. They often get confused and produce impossible predictions (like predicting a 90% chance of a price being lower than a 10% chance).

The Solution: OrderFusion (The "Dance Partner" Model)

The authors created a new model called OrderFusion. Think of it as a model that understands the dance between buyers and sellers.

1. The "Dual Mask" (Filtering the Noise)
In a noisy room, you don't listen to everything everyone said 10 years ago; you listen to what is being said right now. The model uses a "Dual Mask" to ignore old, irrelevant trades and focus only on the most recent interactions. It filters out the "static" so the model can hear the current conversation clearly.

2. The "Iterative Fusion" (The Dance)
This is the core innovation. Instead of looking at buyers and sellers separately, the model puts them in a room together and lets them "talk" to each other repeatedly.

Step 1: The model looks at the buyers.
Step 2: It looks at the sellers.
Step 3: It asks, "How does the buyer's view change if they see what the seller just did?"
Step 4: It updates its understanding.
It repeats this "fusion" process a few times. This allows the model to learn the strategy behind the trades. It realizes, "Ah, when sellers drop their prices, buyers usually jump in immediately."

3. The "Hierarchical Head" (The Organized Family)
When predicting probabilities, a common mistake is "Quantile Crossing." Imagine predicting the weather: you might accidentally predict a 10% chance of rain being higher than a 90% chance of rain. That makes no sense.

The authors built a "Hierarchical Head" that acts like a strict parent. It predicts the middle price first, then builds the higher and lower predictions on top of that middle one, ensuring they never cross over each other. This keeps the math logical and the predictions reliable.

The Results: Small but Mighty

The authors tested their model on electricity markets in Germany (very busy, high traffic) and Austria (less busy, lower traffic).

Accuracy: OrderFusion beat all the other models, including the massive "sledgehammer" AI models and the simple "summary sheet" models. It predicted prices more accurately in both busy and quiet markets.
Efficiency: This is the most impressive part. The massive AI models had millions of parameters (like a brain with millions of neurons). OrderFusion achieved better results with only 4,872 parameters.
- Analogy: It's like building a super-accurate weather forecast using a simple, lightweight pocket calculator instead of a supercomputer. This makes it easy to run on standard laptops, which is great for power companies that need to make quick decisions without expensive hardware.

The Key Takeaway

The paper proves that in electricity markets, how buyers and sellers interact is just as important as what they are trading. By building a model that explicitly simulates this interaction (the "dance") and keeps the math logical (the "strict parent"), we can predict electricity prices better, faster, and with less computing power than ever before.

What the paper does NOT claim:

It does not claim this model can predict prices for next year or next decade. It is strictly for short-term, intraday forecasting.
It does not claim to use weather data or fuel costs (exogenous factors) in this specific version; it relies purely on the orderbook data.
It does not claim to solve all energy problems, but rather provides a better tool for managing the risk of price fluctuations in the short term.

Technical Summary: OrderFusion

Problem Statement

Probabilistic intraday electricity price forecasting is critical for short-term power system operation, particularly as renewable generation and demand-side flexibility increase uncertainty close to delivery times. Unlike day-ahead auction markets, Continuous Intraday (CID) markets operate via the continuous posting of buy and sell orders, creating a dynamic orderbook microstructure.

Current forecasting approaches face two primary limitations:

Loss of Interaction Structure: Conventional methods either aggregate orderbook data into 1D domain features (e.g., Volume-Weighted Average Price, last price) or treat the orderbook as a generic 2D multivariate time series. Both approaches neglect the specific, strategic buy-sell interaction structure inherent in the orderbook.
Quantile Crossing: In probabilistic forecasting, independent estimation of multiple quantiles often leads to "quantile crossing," where higher quantile forecasts fall below lower ones, violating the monotonicity of the predictive distribution. Existing solutions, such as post-hoc sorting, break the end-to-end learning paradigm.

Methodology: OrderFusion

The authors propose OrderFusion, an end-to-end, parameter-efficient deep learning model designed to encode orderbook data while explicitly capturing buy-sell interactions and ensuring non-crossing probabilistic forecasts.

1. Encoding

The model separates the orderbook into buy ( $+$ ) and sell ($-$) sides. Each trade is represented as a triplet of price, volume, and a relative time delta ( $\nabla t$ ) encoding the time remaining until delivery. This results in two variable-length 2D sequences per sample.

2. Backbone Architecture

The backbone processes these sequences through three key components:

Dual Masking Layer: To handle irregular trade counts and prioritize recent information (based on market efficiency hypotheses), the model applies:
- Padding Mask: To align sequences to a maximum length.
- Temporal Mask: To retain only the most recent $L$ trades, discarding older data.
Iterative Fusion Layer: This is the core mechanism for modeling interactions. It employs a series of $K$ $K$ layers where buy-side and sell-side representations are iteratively fused using cross-attention.
- At degree $k=0$ , inputs are projected to a hidden dimension.
- For $k \ge 1$ , the representation of one side (Query) attends to the representation of the opposite side (Key/Value). This allows the model to learn how buyers adjust to sellers and vice versa.
Aggregation Layer: Representations from all interaction degrees ( $k=1$ to $K$ ) are combined via residual connections and aggregated using global average pooling to form a final latent representation.

3. Hierarchical Head

To produce probabilistic forecasts without quantile crossing, the model uses a hierarchical head:

The median quantile ( $\tau=0.50$ ) is predicted directly.
Upper quantiles are predicted as the median plus a non-negative residual.
Lower quantiles are predicted as the median minus a non-negative residual.
This structure enforces monotonicity by construction, eliminating the need for post-hoc correction.

4. Loss Function

The model is trained using Average Quantile Loss (AQL) to jointly estimate multiple quantiles.

Key Contributions

Formulation: The paper frames probabilistic CID price-index forecasting as a microstructure-aware power-system economics problem, emphasizing the need for uncertainty-aware position adjustments.
Model Design: OrderFusion is introduced as a parameter-efficient model that explicitly encodes buy-sell interactions via an iterative cross-attention mechanism, avoiding the parameter bloat of generic time-series models.
Quantile Handling: The methodology introduces a hierarchical head that guarantees non-crossing quantiles within an end-to-end framework.
Empirical Validation: The authors conduct exhaustive experiments across high-liquidity (German) and low-liquidity (Austrian) markets, demonstrating consistent improvements over baselines.

Experimental Results

The model was evaluated on German and Austrian CID markets using rolling window evaluations.

Performance vs. Baselines: OrderFusion outperformed all baselines, including Naïve models, 1D encoding methods (MLP/LQR with VWAP, last price, and exhaustive features), and state-of-the-art 2D time-series models (FEDFormer, iTransformer, PatchTST, TimesNet, TimeXer).
- In the German market, OrderFusion achieved the lowest Average Quantile Loss (AQL) of 3.81 (vs. 4.38 for the next best, TimesNet) and the lowest Mean Absolute Error (MAE) of 9.06.
- In the Austrian market, it achieved an AQL of 5.64 and MAE of 13.52, again ranking first.
Quantile Crossing: OrderFusion achieved an Average Quantile Crossing Rate (AQCR) of 0.00% in all tests, whereas 2D encoding baselines exhibited crossing rates between 1.97% and 4.97%.
Parameter Efficiency: OrderFusion uses only 4,872 parameters, significantly fewer than the 0.87M to 3.38M parameters used by the 2D encoding baselines, making it suitable for resource-constrained operational deployment.
Ablation Studies:
- Removing the dual masking layer increased AQL by 30.51%, highlighting the importance of filtering noise and focusing on recent trades.
- Removing the iterative fusion layer increased AQL by 18.86%, confirming that buy-sell inductive bias is crucial.
- The optimal interaction degree ( $K$ ) was found to be 2; higher degrees offered no significant improvement.
- The hierarchical head successfully eliminated quantile crossing without the computational overhead of post-hoc sorting.

Significance and Claims

The paper claims that OrderFusion addresses the specific challenges of CID markets by moving beyond generic time-series modeling to explicitly model the microstructure of buy-sell interactions. The results suggest that CID markets do not exhibit perfect weak-form efficiency, as historical order flow contains predictive information beyond the last traded price.

The authors emphasize that injecting domain priors (specifically the structure of buy-sell interactions) into the model architecture is more effective than simply stacking parameters. The methodology is presented as a robust, end-to-end solution for operational risk management, capable of generalizing across markets with varying liquidity levels. The authors note that while the model performs well, future work could incorporate exogenous variables (e.g., supply/demand fundamentals) and trades from neighboring delivery periods, though the current scope is strictly limited to orderbook microstructure.