ARMAX Regression More Accurately Determines the Timing of Solar Wind, IMF Bz, Substorms, and ULF Wave Influences on 2 MeV Electron Flux

Simple correlations show influences of solar wind (velocity and number density), IMF Bz, ULF wave power, and substorms (as measured by AE) on 2 MeV electron flux (LANL satellite) over an impressive number of hours and days. However, the diurnal cycle in flux measurements from geosynchronous satellites can inflate correlations, the associations between potential drivers may produce spurious effects, and correlations between all previous hours of a driver may create the appearance that it acts additively over many hours. Autoregressive-moving average transfer function (ARMAX) multiple regressions incorporating previous hours simultaneously can eliminate these cycles and study the impact of each parameter, at each hour, while the others are controlled. Regression coefficients from the ARMAX transfer function are approximately ten times lower than the correlation coefficients, showing that most of the correlation between flux and the possible driving parameters is the result of common cycling behavior. Although both ULF waves and the AE index show sustained positive simple correlations with flux up to 96 h previous, the positive influences measured by the ARMAX technique occur mostly over 1-2 h. Solar wind velocity and the IMF Bz also show most of their influence in the 8 h preceding the flux measurement. Only solar wind number density shows a more sustained action, up to 36 h previous.