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CRPS learning

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  • Berrisch, Jonathan
  • Ziel, Florian

Abstract

Combination and aggregation techniques can significantly improve forecast accuracy. This also holds for probabilistic forecasting methods where predictive distributions are combined. There are several time-varying and adaptive weighting schemes such as Bayesian model averaging (BMA). However, the quality of different forecasts may vary not only over time but also within the distribution. For example, some distribution forecasts may be more accurate in the center of the distributions, while others are better at predicting the tails. Therefore, we introduce a new weighting method that considers the differences in performance over time and within the distribution. We discuss pointwise combination algorithms based on aggregation across quantiles that optimize with respect to the continuous ranked probability score (CRPS). After analyzing the theoretical properties of pointwise CRPS learning, we discuss B- and P-Spline-based estimation techniques for batch and online learning, based on quantile regression and prediction with expert advice. We prove that the proposed fully adaptive Bernstein online aggregation (BOA) method for pointwise CRPS online learning has optimal convergence properties. They are confirmed in simulations and a probabilistic forecasting study for European emission allowance (EUA) prices.

Suggested Citation

  • Berrisch, Jonathan & Ziel, Florian, 2023. "CRPS learning," Journal of Econometrics, Elsevier, vol. 237(2).
    • Handle: RePEc:eee:econom:v:237:y:2023:i:2:s0304407621002724
    DOI: 10.1016/j.jeconom.2021.11.008
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    More about this item

    Keywords

    Combination; Aggregation; Online; Probabilistic; Forecasting; Quantile; Time series; Distribution; Density; Prediction; Splines;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • Q47 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy Forecasting

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