Forecasting geomagnetic activity: Neural networks, moving windows and state transition models

Abstract

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.