Understanding the number of sunspots is crucial for comprehending the Sun’s magnetic-activity cycle and its influence on space weather and the Earth. Recent advancements in machine learning have significantly improved the accuracy of time-series predictions, revealing a compelling approach for sunspot forecasts. Our work takes the pioneering work by proposing a hybrid forecasting approach that combines the Seasonal Autoregressive Integrated Moving Average (SARIMA) with machine-learning algorithms like Random Forest and Support Vector Machine, delivering high prediction accuracy. Despite its high accuracy, we highlight the need for caution in deploying machine-learning-based methods for sunspot-number prediction, demonstrated through a detailed case study with only three extra time stamps leading to a dramatic change. More specifically, when making a forecast of monthly averaged sunspot numbers from 2023–2043 based on data from 1749–2023, we found that the observations in June, July, and August 2023 have a significant impact on the forecast, particularly in the long term. Given the multiseasonal and nonstationary nature of the sunspot time series, we conclude that this kind of phenomenon cannot be simply captured by a pure data-driven model, which can be highly sensitive in the forecast in the long term, and requires a more comprehensive approach, possibly with a model that includes physics.

了解太阳黑子的数量对于理解太阳的磁活动周期及其对太空天气和地球的影响至关重要。机器学习的最新进展显着提高了时间序列预测的准确性，揭示了一种引人注目的太阳黑子预测方法。我们的工作开创性地提出了一种混合预测方法，将季节性自回归综合移动平均线 (SARIMA) 与随机森林和支持向量机等机器学习算法相结合，提供高预测精度。尽管其准确性很高，但我们强调在部署基于机器学习的太阳黑子数预测方法时需要谨慎，这一点通过详细的案例研究证明，仅三个额外的时间戳就会导致巨大的变化。更具体地说，在根据 1749-2023 年的数据对 2023-2043 年的月平均太阳黑子数量进行预测时，我们发现 2023 年 6 月、7 月和 8 月的观测对预测有重大影响，特别是从长期来看。鉴于太阳黑子时间序列的多季节和非平稳性质，我们得出的结论是，这种现象不能简单地用纯数据驱动的模型来捕捉，该模型在长期预测中可能高度敏感，需要更全面的方法，可能有一个包含物理的模型。