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.

中文翻译：

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使用时间序列模型预测长期太阳活动：一些警示性发现

摘要 几个世纪以来对太阳活动的长期预测在模拟气候方面具有重要意义。基于放射性核素的太阳辐照度重建跨越 9.4 到 11.5 千年。有证据表明存在多个最大值和最小值，以及趋势的变化。对数据的分析产生了模棱两可的结果。傅立叶光谱在数据中发现长周期，但这些在时域中未得到证实。自相关函数在几十年的时间里缓慢衰减，表明数据可能无法预测超出这些范围。小波分析表明能量分布在一个频率范围内，因此无法识别固定周期的周期。本文测试时间序列和人工智能模型。预测实验在 44 到 250 年的范围内运行。模型在 44 年时表现相当不错，但在大约 88 年之后，模型无法有效预测。在所有测试的方法中都观察到准确性的下降。尽管在频谱中发现了低频峰值，但包含长周期的模型表现尤其糟糕。模型无法预测更远的地平线，这支持了太阳具有混沌或随机特性的解释。预测与模拟研究一致，在模拟研究中最大值和最小值以不规则的间隔出现，使得它们的时间不可预测。尽管在频谱中发现了低频峰值，但包含长周期的模型表现尤其糟糕。模型无法预测更远的地平线，这支持了太阳具有混沌或随机特性的解释。预测与模拟研究一致，在模拟研究中最大值和最小值以不规则的间隔出现，使得它们的时间不可预测。尽管在频谱中发现了低频峰值，但包含长周期的模型表现尤其糟糕。模型无法预测更远的地平线，这支持了太阳具有混沌或随机特性的解释。预测与模拟研究一致，在模拟研究中最大值和最小值以不规则的间隔出现，使得它们的时间不可预测。