Using the NARMAX OLS-ERR algorithm to obtain the most influential coupling functions that affect the evolution of the magnetosphere

The NARMAX OLS-ERR algorithm, which is widely used in the study of systems dynamics, is able to determine the causal relationship between the input and output variables for nonlinear systems. This technique has been applied to measurements of the solar wind from ACE at L1 and the Dst index in order to find the best solar wind–magnetosphere coupling function, i.e., which combination of solar wind parameters provides the best predictive capabilities of the Dst index. The data-deduced coupling functions were then compared to those suggested in previous analytical and data-based studies. The most appropriate coupling function was found to be n1/2VαBT sin6(θ/2), where the power of velocity, α, was inconclusive but should be in the range 2–3.