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

Masaki Adachi; Masahiro Fujisawa; Michael A Osborne

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arXiv · 2503.06079

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

Masaki Adachi·Masahiro Fujisawa·Michael A Osborne

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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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Masaki Adachi, Masahiro Fujisawa, Michael A Osborne. 2025-03-08. Fixing the Pitfalls of Probabilistic Time-Series Forecasting Evaluation by Kernel Quadrature. https://arxiv.org/abs/2503.06079

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