Paper: arXiv 2507.15079

Authors: Arkadiusz Lipiecki, Bartosz Uniejewski

Abstract

Quantifying the uncertainty of forecasting models is essential to assess and mitigate the risks associated with data-driven decisions, especially in volatile domains such as electricity markets. Machine learning methods can provide highly accurate electricity price forecasts, critical for informing the decisions of market participants. However, these models often lack uncertainty estimates, which limits the ability of decision makers to avoid unnecessary risks. In this paper, we propose a novel method for generating probabilistic forecasts from ensembles of point forecasts, called Isotonic Quantile Regression Averaging (iQRA). Building on the established framework of Quantile Regression Averaging (QRA), we introduce stochastic order constraints to improve forecast accuracy, reliability, and computational costs. In an extensive forecasting study of the German day-ahead electricity market, we show that iQRA consistently outperforms state-of-the-art postprocessing methods in terms of both reliability and sharpness. It produces well-calibrated prediction intervals across multiple confidence levels, providing superior reliability to all benchmark methods, particularly coverage-based conformal prediction. In addition, isotonic regularization decreases the complexity of the quantile regression problem and offers a hyperparameter-free approach to variable selection.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel ‘Isotonic Quantile Regression Averaging’ (iQRA) method, building on established quantile regression frameworks with stochastic order constraints and regularization, indicating advanced mathematical formulation. Empirically, it includes a detailed 10-year study on the German day-ahead electricity market with specific data preprocessing, model architecture (NARX neural networks), rolling-window backtesting, and comparison against multiple state-of-the-art benchmarks using metrics like CRPS and ACE.

Research Flowchart

  flowchart TD
  A["Research Goal: Quantify uncertainty<br/>in electricity price forecasts"] --> B["Methodology: Isotonic Quantile<br/>Regression Averaging iQRA"]

  B --> C["Data: German Day-Ahead<br/>Electricity Market Forecasts"]
  C --> D["Process: Ensemble Point Forecasts<br/>+ Stochastic Order Constraints"]
  
  D --> E["Computation:<br/>Isotonic Regularization<br/>Hyperparameter-Free Selection"]
  E --> F["Output: Probabilistic<br/>Prediction Intervals"]

  F --> G["Key Findings:<br/>Outperforms State-of-the-Art"]
  G --> H["Outcomes: Superior Reliability<br/>& Sharpness across confidence levels"]

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0 of 52 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.