Predicting geostationary 40–150 keV electron flux using ARMAX (an autoregressive moving average transfer function), RNN (a Recurrent Neural Network), and logistic regression: a comparison of models

We screen several algorithms for their ability to produce good predictive models of hourly 40–150 keV electron flux at geostationary orbit (data from GOES-13) using solar wind, Interplanetary Magnetic Field, and geomagnetic index parameters that would be available for real time forecasting. Value-predicting models developed using ARMAX (autoregressive moving average transfer function), RNN (recurrent neural network), or stepwise-reduced regression produced roughly similar results. Including magnetic local time as a categorical variable to describe both the differing levels of flux and the differing influence of parameters improved the models (r as high as 0.814; Heidke Skill Score (HSS) as high as 0.663), however value-predicting models did a poor job at predicting highs and lows. Diagnostic tests are introduced (cubic fit to observation-prediction relationship and Lag1 correlation) that better assess predictions of extremes than single metrics such as root mean square error, mean absolute error, or median symmetric accuracy. Classifier models (RNN and logistic regression) were equally able to predict flux rise above the 75th percentile (HSS as high as 0.667). Logistic regression models were improved by the addition of multiplicative interaction and quadratic terms. Only predictors from 1 or 3 hr before were necessary and a detailed description of flux time series behavior was not needed. Stepwise selection of these variables trimmed non-contributing parameters for a more parsimonious and portable logistic regression model that predicted as well as neural network-derived models. We provide a logistic regression model (LL3: LogisticLag3) based on inputs measured 3 hr previous, along with optimal probability thresholds, for future predictions.