Symmetry-Constrained Forecasting of Periodically Correlated Energy Processes

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 $\tilde{\lambda }(t,\tau )=\frac{1}{2}(1+\rho (t,\tau ))$, where $\rho (t,\tau )$ denotes the local correlation between the current observation and its phase aligned time lag ($\tau$). 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.