Geomagnetic activity shows high degrees of nonlinear variability. The probability distribution has heavy tails, and there are intermittent outliers. This has led to increased interest in forecasting using neural networks and nonlinear regressions, which include time-varying coefficient techniques. Because geomagnetic storms pose the greatest threat to satellites and power grids, there is a particular interest in predicting outlying events. The model proposed here combines two techniques. Neural networks and regressions are trained over moving windows of observations, so that the weights or coefficients adjust to new data. Second, logistic regression is used to predict the periods of high activity, and the cumulative distribution function is used as a causal input in time series and machine learning models. The data set is the Aa index, corrected for secular drift. Forecasting experiments are run over horizons of 1–4 days. The other models include time-varying parameter regressions and a recurrent neural network with fixed weights. The model combining the neural net and logistic regression achieves the most accurate forecast, although the regression is a close second. The ability to predict outliers depends on the width of the moving window. With wider windows, the overall error is lower, but the forecasted values fall into a narrower range, missing the outliers. With narrower windows, the model predicts the outliers better but is vulnerable to calling them at the wrong times, so the average error is higher. Further, while the model achieves more accurate predictions at 1 day, at longer horizons the accuracy deteriorates quite rapidly.

中文翻译：

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预测地磁活动：神经网络、移动窗口和状态转换模型

地磁活动表现出高度的非线性变化。概率分布有重尾，并且存在间歇性异常值。这导致人们对使用神经网络和非线性回归（包括时变系数技术）进行预测的兴趣增加。由于地磁风暴对卫星和电网构成最大的威胁，因此人们对预测外围事件特别感兴趣。这里提出的模型结合了两种技术。神经网络和回归是在移动的观察窗口上进行训练的，以便权重或系数根据新数据进行调整。其次，逻辑回归用于预测高活动时段，累积分布函数用作时间序列和机器学习模型中的因果输入。数据集是 Aa 指数，经过长期漂移校正。预测实验的运行时间为 1-4 天。其他模型包括时变参数回归和具有固定权重的循环神经网络。神经网络和逻辑回归相结合的模型实现了最准确的预测，尽管回归紧随其后。预测异常值的能力取决于移动窗口的宽度。窗口越宽，总体误差越低，但预测值会落入较窄的范围，从而忽略异常值。使用较窄的窗口，模型可以更好地预测异常值，但很容易在错误的时间调用它们，因此平均误差较高。此外，虽然该模型在 1 天时实现了更准确的预测，但在更长的时间范围内，准确性会迅速下降。