Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regression

ArXiv ID: 2404.02270 “View on arXiv”

Authors: Unknown

Abstract

Operational decisions relying on predictive distributions of electricity prices can result in significantly higher profits compared to those based solely on point forecasts. However, the majority of models developed in both academic and industrial settings provide only point predictions. To address this, we examine three postprocessing methods for converting point forecasts of day-ahead electricity prices into probabilistic ones: Quantile Regression Averaging, Conformal Prediction, and the recently introduced Isotonic Distributional Regression. We find that while the latter demonstrates the most varied behavior, it contributes the most to the ensemble of the three predictive distributions, as measured by Shapley values. Remarkably, the performance of the combination is superior to that of state-of-the-art Distributional Deep Neural Networks over two 4.5-year test periods from the German and Spanish power markets, spanning the COVID pandemic and the war in Ukraine.

Keywords: Probabilistic Forecasting, Electricity Prices, Quantile Regression, Conformal Prediction, Isotonic Distributional Regression, Commodities (Energy)

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical methods (quantile regression, conformal prediction, isotonic regression, Shapley values) with significant mathematical formulation, while also demonstrating strong empirical rigor through extensive backtesting on real market data over long periods, including major crises, and comparing against state-of-the-art benchmarks.

  flowchart TD
    A["Research Goal<br>Enhance probabilistic forecasting of<br>day-ahead electricity prices"] --> B["Data: German & Spanish Power Markets<br>4.5-year periods<br>COVID & War in Ukraine"]
    B --> C["Input: Point Forecasts"]
    C --> D["Postprocessing Methods"]
    
    subgraph D [" "]
        direction LR
        D1["Quantile Regression Averaging"]
        D2["Conformal Prediction"]
        D3["Isotonic Distributional Regression"]
    end
    
    D --> E["Ensemble of Predictive Distributions"]
    E --> F["Key Findings"]
    
    subgraph F [" "]
        F1["Isotonic Distributional Regression<br>contributes most via Shapley values"]
        F2["Combination outperforms<br>state-of-the-art Deep Neural Networks"]
        F3["Operational decisions based on<br>predictive distributions yield higher profits"]
    end