Fixing the Pitfalls of Probabilistic Time-Series Forecasting Evaluation by Kernel Quadrature

• URL: http://arxiv.org/abs/2503.06079v1
• Date: Sat, 08 Mar 2025 06:01:10 GMT
• Title: Fixing the Pitfalls of Probabilistic Time-Series Forecasting Evaluation by Kernel Quadrature
• Authors: Masaki Adachi, Masahiro Fujisawa, Michael A Osborne,
• Abstract summary: Most widely used metric, the continuous ranked probability score (CRPS), is a strictly proper scoring function.<n>We found that popular CRPS estimators exhibit inherent estimation biases.<n>We introduce a kernel quadrature approach that leverages an unbiased CRPS estimator and employs cubature construction for computation scalable.
• Score: 19.742371911023774
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Despite the significance of probabilistic time-series forecasting models, their evaluation metrics often involve intractable integrations. The most widely used metric, the continuous ranked probability score (CRPS), is a strictly proper scoring function; however, its computation requires approximation. We found that popular CRPS estimators--specifically, the quantile-based estimator implemented in the widely used GluonTS library and the probability-weighted moment approximation--both exhibit inherent estimation biases. These biases lead to crude approximations, resulting in improper rankings of forecasting model performance when CRPS values are close. To address this issue, we introduced a kernel quadrature approach that leverages an unbiased CRPS estimator and employs cubature construction for scalable computation. Empirically, our approach consistently outperforms the two widely used CRPS estimators.

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