### abstract

- The NARMAX (Nonlinear Autoregressive Moving Average with eXogenous inputs) modeling based approach is used to identify the relations for Solar wind Magnetosphere Coupling Functions in order to identify the one with the best Dst index forecasting abilities. It is argued that the Error Reduction Ratio which is a cornerstone concept in the NARMAX system identification methodology is more appropriate for such nonlinear system as the terrestrial magnetosphere than correlation function analysis which has often been used in the past. It is shown that the identified relationships for coupling functions are proportional to $\sin\left(\frac{\theta}{2}\right)^{6}$, where $\theta$ is the clock angle, and not to $\sin\left(\frac{\theta}{2}\right)^{4}$ as was suggested in earlier studies. It is shown that the factor $\sin\left(\frac{\theta}{2}\right)^{6}$ appears naturally within the analytical model of Kan and Lee (1979) as the dependence on the clock angle.