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Online Aggregation of Probabilistic Predictions of Hourly Electrical Loads

  • MATHEMATICAL MODELS AND COMPUTATIONAL METHODS
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Abstract

In this paper, we consider the problem of online probabilistic time series forecasting. The difference between a probabilistic prediction (distribution function) and a numerical outcome is measured using a loss function (scoring rule). In practical statistics, the Continuous Ranked Probability Score (CRPS) rule is often used to estimate the discrepancy between probabilistic predictions and quantitative outcomes. Here, we consider the case when several competing methods (experts) give their predictions in the form of distribution functions. Expert predictions are provided with confidence levels. We propose an algorithm for online aggregation of these distribution functions with allowance for the confidence levels to expert forecasts. The discounted error of the proposed algorithm with allowance for the confidence levels is estimated in the form of a comparison of the cumulative losses of the algorithm and the losses of experts. A technology for constructing predictive expert algorithms and aggregating their probabilistic predictions using the example of the problem of predicting electricity consumption 1 or more hours ahead was developed. The results of numerical experiments using real data are presented.

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Notes

  1. Here, 1u ≥ y = 1 if u ≥ y, and it is 0 otherwise.

  2. The nature of these sets will be specified later.

  3. The distribution function is non-decreasing function F(y) defined on interval [a, b] such that F(a) = 0 and F(b) = 1. It is also continuous on the left and has a limit on the right at every point.

  4. This statement was proposed in [22] and further developed in [1].

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Funding

This work was partially supported by the Russian Foundation for Basic Research, grant no. 20-01-00203.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, 127051, Moscow, Russia

    V. V. V’yugin & V. G. Trunov

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  1. V. V. V’yugin
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  2. V. G. Trunov
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Correspondence to V. V. V’yugin.

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The authors declare that they do not have a conflict of interest.

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Translated by A. Ivanov

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V’yugin, V.V., Trunov, V.G. Online Aggregation of Probabilistic Predictions of Hourly Electrical Loads. J. Commun. Technol. Electron. 67, 702–716 (2022). https://doi.org/10.1134/S1064226922060201

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  • DOI: https://doi.org/10.1134/S1064226922060201

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