Combining frequency and time domain models to forecast space weather

Space weather series incorporate several distinct components, cycles at multiple frequencies, irregular trends, and nonlinear variability. The cycles are stochastic, i.e., the amplitude varies over time. Similarly, the trend is stochastic: the slope and direction of trending change repeatedly. This study sets out a combined model using both frequency and time domain methods, in two stages. In the first stage, a frequency domain algorithm is estimated and forecasted. In the second stage, the forecast is used as an input in a neural network. The combined model also includes a term enabling the model to react inversely to large deviations between the actual values and forecast. The models are evaluated using two data sets, the hemispheric power data obtained from the Polar Orbiting Environment satellites, and the Aa geomagnetic index. All the series are at a daily resolution. Forecasting experiments are run over horizons of 1–7 days. The models are estimated using a moving window or adaptive approach. The combined model consistently achieves the most accurate results. Among single equation methods, the frequency domain model is more accurate for the geomagnetic index because it is able to capture the underlying cycles more effectively. In the hemispheric power series, the cycles are less pronounced, so that time domain methods are more accurate, except at very short horizons. Nevertheless, in both data sets, the combined model works well because the frequency domain algorithm captures cyclical behavior, while the neural net is better able to capture short-term dependence and trending.