Paper: arXiv 2604.19580

Authors: Simon Hirsch, Florian Ziel

Abstract

Electricity price forecasting supports decision-making in energy markets and asset operation. Probabilistic forecasts are increasingly adopted to explicitly quantify uncertainty, typically issued as quantile predictions or ensembles of the full predictive distribution. However, how improvements in statistical forecast quality translate into economic value remains unclear. Battery storage arbitrage in day-ahead markets is a popular application-based benchmark for this purpose. We analyze quantile-based trading strategies (QBTS) and identify two critical flaws: they do not incentivize honest probabilistic forecasting and they ignore the intertemporal dependence structure of electricity prices. We therefore frame battery optimization as a stochastic program based on fully probabilistic forecasts and examine decision quality measurement for risk-neutral and risk-averse settings under different uncertainty models. Our discussion touches both sides of the coin: How reliable is the economic evaluation of forecasting models though (simplified) application studies - and how do improvements in statistical forecast quality for stochastic programs relate to the decision-quality and economic performance? We provide theoretical justification and empirical evidence from a case study on the German electricity market. Our results highlight the pitfalls of ranking forecasting models through battery trading strategies. We conclude with implications for evaluation practice and directions for future research in application-based forecast assessment.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10 (capped from 8.0: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper combines rigorous stochastic programming theory, scoring rule analysis, and multivariate dependency modeling with a comprehensive case study on the German electricity market. It effectively bridges the gap between theoretical probabilistic forecasting properties and practical, data-driven backtesting of battery trading strategies.

Research Flowchart

  flowchart TD
    A[Research Goal: Relate Forecast Quality to Economic Performance] --> B[Input: German Electricity Market Data]
    B --> C[Method: Compare Quantile-based Trading vs. Stochastic Programming]
    C --> D[Process: Battery Arbitrage Optimization]
    D --> E[Analysis: Impact of Uncertainty & Risk Sensitivity]
    E --> F[Outcome: Pitfalls of Battery-based Model Ranking]
    F --> G[Implications: New Standards for Forecast Evaluation]

Cited References (107)

  1. A scoring system for probability forecasts of ranked categories (1969)
  2. Event-based evaluation of electricity price ensemble forecasts (2021)
  3. Solving the problem of inadequate scoring rules for assessing probabilistic football forecast models (2012)
  4. Evaluating probabilistic forecasts of football matches: the case against the ranked probability score (2021)
  5. Beyond strictly proper scoring rules: The importance of being local (2021)
  6. K-nearest neighbour classifiers-a tutorial (2021)
  7. Asymmetric penalties underlie proper loss functions in probabilistic forecasting (2025) — link
  8. Discrimination ability of the energy score (2013)
and 99 more
  1. Recent advances in electricity price forecasting: A review of probabilistic forecasting (2018)
  2. The Kendall and Mallows kernels for permutations (2015)
  3. A new measure of rank correlation (1938)
  4. Correlation kernels for support vector machines classification with applications in cancer data (2012)
  5. Conditional copulas, association measures and their applications (2011)
  6. Multivariate forecasting evaluation: On sensitive and strictly proper scoring rules (2019) — link
  7. Regularized quantile regression averaging for probabilistic electricity price forecasting (2021)
  8. The value of coordination in multimarket bidding of grid energy storage (2023)
  9. Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regression (2024)
  10. The profitability of energy storage in European electricity markets (2021)
  11. Stochastic optimization of trading strategies in sequential electricity markets (2023)
  12. Maximising the value of electricity storage (2016)
  13. Stochastic search for a parametric cost function approximation: Energy storage with rolling forecasts (2024)
  14. Value-oriented forecast reconciliation for renewables in electricity markets (2025)
  15. Probabilistic forecasting with a hybrid Factor-QRA approach: Application to electricity trading (2024)
  16. Economic and statistical measures of forecast accuracy (2000)
  17. Higher order elicitability and Osband’s principle (2016)
  18. Order-sensitivity and equivariance of scoring functions (2019)
  19. Evaluating the discrimination ability of proper multi-variate scoring rules (2024)
  20. An empirical analysis of scenario generation methods for stochastic optimization (2016)
  21. Regions of reliability in the evaluation of multivariate probabilistic forecasts (2023)
  22. Expected shortfall is jointly elicitable with value at risk-implications for backtesting (2015) — link
  23. Robust forecast evaluation of expected shortfall (2020)
  24. Loss functions in regression models: Impact on profits and risk in day-ahead electricity trading (2025)
  25. Optimising quantile-based trading strategies in electricity arbitrage (2025)
  26. Conformal prediction for electricity price forecasting in the day-ahead and real-time balancing market (2025)
  27. Conformal Prediction Techniques for Electricity Price Forecasting (2024)
  28. Combining predictive distributions of electricity prices: Does minimizing the CRPS lead to optimal decisions in day-ahead bidding? — → 2308.15443
  29. Optimizing Energy Storage Profits: A New Metric for Evaluating Price Forecasting Models (2024)
  30. Forecasting Electricity Prices With Decision-Focused Learning for Storage Optimization (2025)
  31. Electricity price prediction for energy storage system arbitrage: A decision-focused approach (2022)
  32. Smoothing quantile regression averaging: A new approach to probabilistic forecasting of electricity prices (2025)
  33. Analyzing Uncertainty Quantification in Statistical and Deep Learning Models for Probabilistic Electricity Price Forecasting (2025) — link
  34. Ranking probabilistic forecasting models with different loss functions (2024) — link
  35. Extrapolating the long-term seasonal component of electricity prices for forecasting in the day-ahead market — → 2503.02518
  36. Stock portfolio selection using learning-to-rank algorithms with news sentiment (2017)
  37. Constructing long-short stock portfolio with a new listwise learn-to-rank algorithm (2022)
  38. Distributional neural networks for electricity price forecasting (2023)
  39. Probabilistic multivariate electricity price forecasting using implicit generative ensemble post-processing (2020)
  40. Multivariate probabilistic forecasting of electricity prices with trading applications (2025)
  41. Multiple split approach–multidimensional probabilistic forecasting of electricity markets — → 2407.07795
  42. Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting — → 2504.02518
  43. Risk measures: robustness, elicitability, and backtesting (2022)
  44. Optimization of conditional value-at-risk (2000)
  45. Conditional value-at-risk: optimization approach (2001)
  46. Statistical and economic evaluation of forecasts in electricity markets: beyond RMSE and MAE — → 2511.13616
  47. The utility of wealth (1952)
  48. Portfolio Selection (1952)
  49. Comparing predictive accuracy, twenty years later: A personal perspective on the use and abuse of Diebold–Mariano tests (2015)
  50. Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate modeling frameworks (2018)
  51. Comparing predictive accuracy (2002)
  52. Aligning the Evaluation of Probabilistic Predictions with Downstream Value (2025) — link
  53. Addressing the loss-metric mismatch with adaptive loss alignment (2019)
  54. Automatic loss function search for predict-then-optimize problems with strong ranking property (2022)
  55. Smart “predict, then optimize” (2022)
  56. Task-based end-to-end model learning in stochastic optimization (2017)
  57. Strictly proper scoring rules, prediction, and estimation (2007)
  58. Modeling public holidays in load forecasting: a German case study (2018)
  59. Weighted scoringrules: Emphasizing particular outcomes when evaluating probabilistic forecasts (2024)
  60. Evaluating forecasts for high-impact events using transformed kernel scores (2023)
  61. Weighted verification tools to evaluate univariate and multivariate probabilistic forecasts for high-impact weather events (2023)
  62. Generic conditions for forecast dominance (2021)
  63. How to Compare Copula Forecasts? (2024) — link
  64. Estimation of the continuous ranked probability score with limited information and applications to ensemble weather forecasts (2018)
  65. Variogram-based proper scoring rules for probabilistic forecasts of multivariate quantities (2015)
  66. Coherent dispersion criteria for optimal experimental design (1999)
  67. Pyomo: modeling and solving mathematical programs in Python (2011)
  68. Parallelizing the dual revised simplex method (2018)
  69. Mutual fund performance (1966)
  70. Downside risk (1991)
  71. A data-driven merit order: Learning a fundamental electricity price model — → 2501.02963
  72. Hierarchical forecasting for aggregated curves with an application to day-ahead electricity price auctions — → 2305.16255
  73. From day-ahead to mid and long-term horizons with econometric electricity price forecasting models (2025)
  74. Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark (2021)
  75. Deep distributional time series models and the probabilistic forecasting of intraday electricity prices (2023)
  76. Optimal portfolio choice with parameter uncertainty (2007)
  77. Trading at EPEX SPOT (2025) — link
  78. Generalized additive models for location, scale and shape (2005)
  79. Distributional modeling and short-term forecasting of electricity prices by generalized additive models for location, scale and shape (2011)
  80. Forecasting the intra-day spread densities of electricity prices (2020)
  81. Online distributional regression (2024) — link
  82. Government Gas Conversion Factors for Company Reporting - Methodology Paper for Conversion factors Final Report (2024) — link
  83. Probabilistic forecasting in day-ahead electricity markets: Simulating peak and off-peak prices (2020)
  84. Techniques for Verifying the Accuracy of Risk Measurement Models (1995)
  85. Optimal bidding in hourly and quarter-hourly electricity price auctions: Trading large volumes of power with market impact and transaction costs (2022)
  86. The value of probabilistic forecasts for electricity market bidding and scheduling under uncertainty (2024)
  87. Bidding and scheduling in energy markets: Which probabilistic forecast do we need? (2022)
  88. The Impact of Load Forecasting Model Choice on the Economic Operation of Industrial Energy Storage (2025)
  89. Assessing the calibration of multivariate probabilistic forecasts (2024)
  90. Probabilistic forecasts, calibration and sharpness (2007)
  91. Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds (2008)
  92. Assessing the calibration of high-dimensional ensemble forecasts using rank histograms (2016)
  93. Local scale invariance and robustness of proper scoring rules (2023)
  94. Localizing strictly proper scoring rules (2025)
  95. Minimum scoring rule inference (2016)
  96. Beyond error measures to the utility and cost of the forecasts (2021)
  97. Data-driven Calibration Sample Selection and Forecast Combination in Electricity Price Forecasting: An Application of the ARHNN Method (2025) — link
  98. Scenario reduction in stochastic programming (2003)
  99. The energy distance for ensemble and scenario reduction (2021)

7 of 107 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.