Forecasting long-term solar activity with time series models: Some cautionary findings

Abstract

Long-term forecasting of solar activity, over a scale of centuries, is of interest in modeling climate. Reconstructions of solar irradiance based on radionuclides span 9.4 to 11.5 millennia. There is evidence of multiple maxima and minima, as well as changes in trend. Analysis of the data yields ambiguous results. Fourier spectra find long cycles in the data, but these are not confirmed in the time domain. The autocorrelation function decays slowly over a period of several decades, indicating that the data is probably not predictable beyond these horizons. Wavelet analysis indicates that the energy is spread out over a range of frequencies, making it impossible to identify cycles at fixed periodicities. This paper tests time series and artificial intelligence models. Forecasting experiments are run over horizons ranging from 44 to 250 years. At 44 years the models do reasonably well, but beyond about 88 years, the models do not forecast effectively. The deterioration in accuracy is observed in all the methods tested. Despite the finding of low-frequency peaks in the spectrum, models incorporating long cycles do particularly badly. The failure of the models to predict at longer horizons supports the interpretation that the sun has chaotic or stochastic properties. The forecasts are consistent with simulation studies in which maxima and minima occur at irregular intervals, making their timing unpredictable.