Yu and Bunn beat every benchmark, with the one-sided Diebold-Mariano test rejecting equal accuracy at p below 0.05 in every comparison. The source of that advantage remains unresolved. Three changes arrive together: orders from neighboring delivery products, learned dynamic masking, and a target that shifts from aggregated price indices to buy-sell price trajectories. Isolating the first two requires an ablation. The paper provides none.
What OrderFusion+ sees
The market is German continuous intraday trading in 15-minute delivery products. Trading begins at 15:00 on the previous day and closes 30 minutes before delivery at exchange level. Nothing executes during the final five minutes. Because several delivery products trade in parallel, a trader at 15:00 can quote the 18:00, 19:00 and 20:00 products simultaneously. The paper starts from that overlap: an order for a distant product may reveal something about a nearer one, following the cross-product price dependencies documented by Hirsch and Ziel.
The target is the larger departure. EPEX publishes ID3, ID2 and ID1, volume-weighted average prices over the final three, two and one hours. Each reduces the full trading path to a single number. Yu and Bunn forecast the sequence of 15-minute VWAPs instead, separating the buy and sell sides and estimating quantiles 0.1, 0.5 and 0.9. They test three forecast origins, 180, 120 and 60 minutes before delivery, with corresponding forecast lengths of 180, 120 and 60 minutes.
The architecture stays compact. Side-specific order features, comprising price, volume, time position and product position, first pass through 1x1 convolutions. Masked cross-attention then allows each side to attend to the other, with weights shared across two passes. Between those passes, the dynamic mask sampling layer chooses one of 30 masks for each side and sample. Its bank combines historical windows of 15, 30, 60, 120 and 180 minutes with neighbor counts of 0, 1, 2, 4, 8 or 12.
At the 180-minute origin, the full model has 41,124 trainable parameters. Training takes 25 to 35 minutes on one A100, while inference finishes in under a second. The data are commercial EPEX order histories beginning in January 2022, arranged into three rolling folds, with test coverage spanning all of calendar 2024.
The 10.62 EUR/MWh result survives comparison
OrderFusion+ records average quantile loss of 10.62 EUR/MWh. The same-input Transformer reaches 11.72, the LSTM 11.79, zero-shot TabPFN-TS 12.05 and the strongest persistence rule 12.07. It also leads all thirteen models on the point metrics, with MAE 28.04, RMSE 101.76 and R-squared 0.39. The one-sided Diebold-Mariano test with the Harvey correction rejects equal accuracy against every baseline at p below 0.05. Quantile crossing never occurs, compared with 3.09% for LQR. Fig. 5 shows OrderFusion+ leading at each of the three origins.
The persistence results say more than the broader model table. Persistence-2 repeats the latest 30-minute VWAP forward and produces AQL 12.07 with R-squared 0.32. Its 15-minute counterpart is weaker at 12.87, and the 60-minute rule deteriorates to 21.00. Reusing the previous-day path fares worst at 21.95 and R-squared minus 0.59. Recent trades averaged over 30 minutes therefore form the strongest naive signal. OrderFusion+ lowers loss by roughly 12%, equivalent to 1.45 EUR/MWh.
Do neighboring delivery products help?
The evidence separates from the claim at this point. Support for the masking mechanism comes from the distribution of masks selected by the fitted model. Across all testing samples and the three origins, the modal historical window is 30 minutes, chosen for 63% of samples, while the modal neighbor count is zero at 47%. As the origin moves from minus 180 to minus 60, the modal window shortens from 30 to 15 minutes. The authors interpret that shift as evidence that information concentrates in the most recent trades near delivery. The reading is plausible. Yet on both axes, the modal setup resembles Persistence-2 with no neighbors at all.
We did not find an ablation anywhere in the paper that restricts the product dimension to one and reports the loss delta. Nor did we find one replacing sampled masking with a fixed 30-minute window. In their absence, the full 1.45 EUR/MWh belongs to the architecture as a whole, including side-specific cross-attention, trajectory targets, calendar embeddings and masked quantile loss. The chosen-mask histogram records what one fitted model selected. It cannot allocate the gain among those components.
The authors identify this weakness themselves. Appendix B retrains OrderFusion+ "with the same protocol using another random seed". The resulting accuracy is statistically identical: "the testing AQL of the two models does not differ significantly (10.62 versus 10.70), as indicated by p-value > 0.05". They call this a Rashomon effect and warn that "the side-specific distributions should not be interpreted as a fixed market conclusion."
Figures 6 and 7 show that the second seed chooses a different mask distribution from the first. The authors argue that cross-attention can move information selected on one side to the other, allowing different allocations to perform the same function. Fair enough. The abstract's promise of "insights into market efficiency" consequently depends on a quantity that the paper itself says should not be treated as a fixed market conclusion. Two findings persist across seeds: the 30-minute share across all testing samples, 63% versus roughly 65%, and the shortening of the modal window from 30 to 15 minutes as the origin approaches. The paper says the second seed confirms both. They are also the findings that echo the naive benchmark.
TimesFM 3.0 (330M parameters) trails a 30-minute VWAP
TimesFM 3.0 has 330.7M parameters and reaches AQL 14.85, compared with 12.07 for the 30-minute VWAP rule. Chronos-2 (119.5M) ranks last among the four foundation models at 19.05, while Moirai 2.0 reaches 17.66. TabPFN-TS (58.0M) performs best of the four at 12.05. Even so, the DM test finds no significant advantage over Persistence-2, and its average quantile coverage error is 8.62%.
Model size carries no performance signal here.
The paper concludes that "generic pretrained foundation models are insufficient for probabilistic intraday price trajectory forecasting". These comparisons use zero-shot models without fine-tuning, though that objection has limited force under the authors' own premise that such models "have shown strong zero-shot forecasting performance in unseen domains".
Trading relevance remains less settled. Calibration trails the trivial rules: AQCE is 2.29% against 0.33% for the best persistence rules, with the four spanning 0.33 to 0.70 in Table 3. Yu and Bunn describe OrderFusion+ as best among the non-persistence baselines and worse than persistence. An RMSE of 101.76 beside an MAE of 28.04 suggests heavy-tailed errors, but the paper does not examine that tail. It estimates only three quantiles, "to demonstrate functionality".
The trading motivation draws on Marcjasz and Semmelmann-style threshold rules, then ends at forecast losses. There is no P&L and no spread assumption. The experiment that would change my view is whether 1.45 EUR/MWh of quantile-loss improvement remains after execution. Across all testing samples, the model's own modal input is the latest 30 minutes of trades with no neighboring products, at 63% and 47% respectively.
We could not test any of this ourselves. The mechanism requires order-level interactions between buys and sells across parallel delivery products. EPEX Continuous Anonymous Orders History costs 3,900 EUR per calendar year for internal use, or 325 EUR per month. Our holdings consist of daily and one-minute OHLCV, without an order book or electricity delivery contracts, so reproduction is impossible for us. Our earlier work on European long-term transmission rights concerns auction-level data rather than the intraday book (earlier note).
The authors list three limitations: an empirical mask grid, unexplored weather features and reliance on a single market. A fourth would be inexpensive to resolve. Set the neighbor count to zero, retrain, and report the AQL.