Logistic Regression as an Alternative to Neural Networks or ARMAX for Predicting GOES-13 40-150 keV Electron Flux

Both a recurrent neural network (RNN) and a logistic regression containing multiplicative interaction and quadratic terms predicted hourly 40-150 keV electron flux at geosynchronous orbit well (Heidke skill score as high as 0.778 for flux rise above the 75th percentile). Predictors included easily available solar wind, IMF, and geomagnetic index parameters up to 48 hours previous. Solar wind velocity, number density and pressure, IMF Bz, and Dst were tested although not all were found to be useful. Including magnetic local time (MLT) as a predictor in the logistic regression, or creating separate RNN models for each MLT, increased predictive ability. Logistic regression has several advantages over RNN: 1) Stepwise logistic regression, by limiting predictors to those that are statistically significant, reduces the model down to the minimum necessary for good prediction, both in terms of knowing which parameters are useful and which hours are most predictive. While this does occur within the RNN, the trimming, if done by the algorithm, is not obvious, or, if done by hand, not easily accomplished or optimized. 2) The ability to incorporate MLT as a term in the logistic model is a more efficient method than creating separate RNN models for each MLT. 3) The coefficients of the logistic regression prediction equation are more easily transported to other devices. 4) There may, potentially, be some scientific value in understanding which parameters are most predictive. Logistic regression gives a more definitive answer to this question than a neural network.

We also modelled electron flux time series behavior using the ARMAX (autoregressive moving average transfer function) technique, on the assumption that understanding the cycling behavior would increase predictive ability. However, this did not provide any improvement. While simple correlations show what appear to be long term flux responses to many parameters, these strong associations are mostly the result of co-cycling or co-trend behavior between predictor and flux. Consequently, modelling this behavior only moves their description to other terms and does not change prediction output. The logistic regression more easily addresses this time series behavior with the MLT terms and allows prediction using information 1-3 hours prior to flux rather than a longer time series.