Symmetry-constrained forecasting of periodically correlated energy processes

Cyril Voyant, Candice Banes, Luis Garcia-Gutierrez (), Gilles Notton (), Milan Despotovic and Zaher Mundher Yaseen
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Cyril Voyant: Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris Sciences et Lettres
Luis Garcia-Gutierrez: Università di Corsica Pasquale Paoli [Université de Corse Pascal Paoli], SPE - Laboratoire « Sciences pour l’Environnement » (UMR CNRS 6134 SPE) - CNRS - Centre National de la Recherche Scientifique - Università di Corsica Pasquale Paoli [Université de Corse Pascal Paoli]
Gilles Notton: SPE - Laboratoire « Sciences pour l’Environnement » (UMR CNRS 6134 SPE) - CNRS - Centre National de la Recherche Scientifique - Università di Corsica Pasquale Paoli [Université de Corse Pascal Paoli]
Milan Despotovic: University of Kragujevac

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Abstract: Time series in energy systems, such as solar irradiance, wind speed, or electrical load, are characterized by strong diurnal and seasonal periodicities. Accurate forecasting requires accounting for time varying statistical properties that stationary or classical persistence models cannot capture. A family of analytical forecasting operators for cyclostationary processes is introduced, extending persistence through a closed form coefficient , where ρ(t, τ) denotes the local correlation between the current observation and its phase aligned time lag (τ). This formulation preserves periodic variance and covariance, achieving a symmetry induced reduction of effective degrees of freedom. The resulting operator defines a training free analytical limit of persistence under periodic non stationarity. Validation on synthetic cyclostationary signals and empirical renewable energy datasets demonstrates consistent accuracy gains over classical persistence, particularly at multi hour horizons. By embedding temporal symmetry into the prediction process, the framework provides a physically interpretable, reproducible, and computationally minimal baseline for forecasting periodic processes across energy and complex systems.

Date: 2026-09
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Published in Applied Mathematical Modelling, 2026, Lecture Notes in Electrical Engineering, 157, pp.116988. ⟨10.1016/j.apm.2026.116988⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05611542

DOI: 10.1016/j.apm.2026.116988

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