Organizations: Department of Computational Social Science, Wrocław University of Science and Technology, Poland · Indicio Technologies AB, Stockholm, Sweden · Department of Operations Research and Business Intelligence, Wrocław University of Science and Technology, Poland
Day-ahead electricity price forecasts support trading and storage decisions, but for battery arbitrage predicting intraday price spreads is more relevant than predicting individual hourly prices. Here we show that a temporal hierarchy forecasting (THieF) framework that jointly reconciles forecasts of hourly electricity prices and all intraday price spreads consistently improves performance across two major European electricity markets and three different forecasting architectures. Using five years of out-of-sample data from Germany and Spain, we obtain accuracy improvements of up to 19.7% and profit gains of up to 10.4% relative to unreconciled hourly price forecasts. The gains persist even for a highly accurate pretrained TabPFN foundation model. Our results demonstrate that exploiting coherent relationships between economically relevant forecasting targets can improve both predictive accuracy and decision value, and that better statistical forecasts do not necessarily imply better economic decisions.
Figures & tables
Figure 1: The summing matrices Sblock ( left panel ) and Sspread ( right panel ) defined in Eq. ( 4 ) and Eq. ( 9 ), respectively. Blue blocks denote positive elements with shading indicating weights ranging from 241 for S24 to 1 for S1 , while red blocks denote negative values equal to −1 . The weights occurring in each submatrix are annotated in its top-right corner.
Figure 2: Top two panels: German (DE) and Spanish (ES) day-ahead electricity prices from 5 January 2018 to 31 December 2025. Middle panels: Day-ahead load forecasts in both countries. Bottom panel: Day-ahead renewable generation forecasts in both countries, including total wind generation and solar generation. The shaded area indicates the initial training window used for generating forecasts for the first day of the test period, 1 January 2021.
RMSE
dRMSE
MAE
dMAE
SSRMSE
SSdRMSE
SSMAE
SSdMAE
Germany
Base
35.92
28.19
23.65
19.18
—
—
—
—
Block THieF
34.89
27.22
22.97
18.65
2.9%
3.4%
2.9%
2.8%
ARX
Spread THieF
30.49
22.71
19.77
15.39
15.1%
19.4%
16.4%
19.7%
Base
29.58
22.06
18.21
14.03
—
—
—
—
Block THieF
28.10
20.26
17.29
12.94
5.0%
8.2%
5.0%
7.8%
Table 1: Forecast evaluation measures for all three models (ARX, NARX and TabPFN) and forecasting frameworks (Base, Block THieF and Spread THieF) over the 5-year test period in the German and Spanish markets; see Sec. 5.1 for error metric definitions. The coloring is applied jointly for all Skill Scores. For each forecasting model, Spread THieF significantly outperforms both Base and Block THieF at the 1% level under both absolute-error and squared-error loss, according to the CPA test; see Sec. 5.2 for details.
ARX
NARX
TabPFN
ARX
NARX
TabPFN
Germany
Spain
η=1
Base (hours)
150,281
148,743
151,350
80,118
77,552
80,410
Base (spreads)
149,442
149,662
147,815
80,616
79,796
78,055
Block THieF
151,211
149,448
151,662
80,272
77,975
80,140
Spread THieF
153,274
154,265
153,485
81,704
81,859
81,000
Table 2: Total profits (EUR) from the BESS trading strategy for all three models (ARX, NARX, and TabPFN) and the considered forecasting frameworks over the 5-year test period in the German and Spanish markets. Note that for efficiency η<1 the decisions cannot be recovered from forecasts of the unadjusted spreads alone. The coloring is applied separately for each market and efficiency. For comparison, we report the profits for the Oracle strategy, which assumes perfect foresight, and the strategy based on Naive price forecasts; see Sec. 5.3 and 5.4 for details.
Figure 3: Rolling RMSE over a 180-day window in the German ( top ) and Spanish ( bottom ) markets. The solid lines mark the RMSE of the Spread THieF approach for the three models. The lighter shaded areas of the same color extend from the Spread THieF value to the corresponding Base value, so that their width represents the improvement obtained from reconciliation. Values for 29.06.2021 are the RMSE for 1.01-29.06.2021, i.e., the light gray shaded area on the left, values for 30.06.2021 are the RMSE for 2.01-30.06.2021, etc. The gray line at the bottom of each plot shows the day-ahead price series, rescaled for visualization and with extreme prices annotated.
Figure 4: Rolling Relative Opportunity Cost (ROC) over a 180-day window in the German ( top ) and Spanish ( bottom ) markets, and battery efficiency η=1 . The solid lines mark the ROC of the Spread THieF approach for the three models. The lighter shaded areas of the same color extend from the Spread THieF value to the corresponding Base value, so that their width represents the improvement obtained from reconciliation. Values for 29.06.2021 are the ROC scores for 1.01-29.06.2021, i.e., the light gray shaded area on the left, values for 30.06.2021 are the ROC scores for 2.01-30.06.2021, etc. The gray line at the bottom of each plot shows the day-ahead price series, rescaled for visualization and with extreme prices annotated. The elevated rolling ROC for TabPFN in the German market in the second half of 2023 is largely driven by a single trading decision, see Fig. 5 .
Figure 5: Example of trading decisions in the German day-ahead market on Sunday 2 July 2023, when the price reached its minimum over the test period, falling to −500.00 EUR/MWh in hour 15. Dashed lines represent realized prices, which are used by the perfect-foresight Oracle benchmark, while solid lines show TabPFN-2 predictions. Colored triangles indicate trading decisions, with green denoting a profitable trade and red a loss. Based on the unreconciled hourly forecasts, TabPFN selects hour 15 as the selling hour, resulting in a single-day loss exceeding 300 EUR for the 1 MWh BESS. In contrast, Spread THieF adjusts the predicted daily price profile sufficiently to avoid this costly trading decision and instead yields a positive profit.
Foundation models promise accurate forecasts with little or no task-specific training, but whether they can replace models designed specifically for electricity price forecasting remains unclear. We compare nine variants from five foundation model families, evaluated in zero-shot mode, with two state-of-the-art electricity price forecasting benchmarks in Germany, Poland, and Spain over 2021-2025. Their performance is assessed in terms of point and probabilistic forecasting accuracy, as well as economic value in battery energy storage arbitrage. Only the TabPFN models consistently and significantly outperform the benchmarks across all three markets and all statistical measures. However, this statistical dominance does not translate directly into economic dominance: TabPFN performs best under unlimited bids and riskier quantile-based strategies, whereas the Distributional Deep Neural Network benchmark is more profitable when risk tolerance is lower. Thus, foundation models cannot universally replace market-specific models, and their value depends on both model architecture and the decision problem.
Arkadiusz Lipiecki, Rafał Weron
Department of Computational Social Science, Wrocław University of Science and Technology, Poland · Department of Operations Research and Business Intelligence, Wrocław University of Science and Technology, Poland · Center for Research in Energy (CoRE), Aarhus University, 8000 Aarhus C, Denmark
Accurate and efficient imbalance electricity price forecasting is critical for industrial energy trading systems, especially as battery assets and automated bidding pipelines increasingly participate in balancing markets. However, real-time forecasting is complicated by nonlinear market-rule-based price formation, heterogeneous input signals, and incomplete data availability caused by communication delays, publication lags, and measurement outages. This paper proposes a market-rule-informed neural forecasting framework that embeds imbalance price formation rules into the latent space of an expressive neural network. The proposed framework preserves raw signal information while exploiting transparent market-rule priors. We further analyze operational robustness by removing price-component information and characterize how forecasting performance scales with input length and forecasting horizon. Experimental results show that the proposed model achieves competitive forecasting performance with substantially fewer trainable parameters and shorter training time than generic deep learning baselines. Experimental results show that the proposed model achieves competitive forecasting performance with substantially fewer trainable parameters and shorter training time than generic deep learning baselines, demonstrating that market-rule priors and expressive neural networks should be jointly used for accurate and computationally sustainable forecasting in industrial energy trading applications. The implementation is publicly available at https://runyao-yu.github.io/MRINN/.
Runyao Yu, Julia Lin, Derek W. Bunn +6
Delft University of Technology · Austrian Institute of Technology · London Business School +2
Recent advances in Time Series Foundation Models (TSFMs) promise zero-shot forecasting capabilities with minimal task-specific training. While these models have shown strong performance across generic benchmarks, their applicability in volatile, complex electricity markets remains underexplored. Addressing this gap, this study provides a systematic empirical evaluation of several TSFMs, specifically Chronos-2 and Chronos-Bolt (developed by Amazon), and TimesFM 2.5 (provided by Google), for forecasting Belgian day-ahead and imbalance electricity prices. For both considered markets, Chronos-2 in ARX mode produces the most accurate forecasts. Compared with the best ensemble prediction from other machine learning methods, Chronos-2's Mean Absolute Error (MAE) is 5% lower for the day-ahead market. In contrast, the model yields 10% higher MAE predicting imbalance prices across all forecast horizons, except for the two-hour-ahead horizon. Moreover, we find that TSFMs exhibit genuine zero-shot forecasting skills but still struggle under extreme market conditions.
Chi Bui, Maria Margarida Mascarenhas, Arnaud Verstraeten +1