The method of Klimas et al. [1997> for constructing dynamical analogues of physical input-output systems is generalized. Higher-order analogues with sensitivity to more features of the input data are derived. Solar wind VBs parameter data are used for input and Dst index data are used for output to construct analogues of the magnetospheric dynamics responsible for Dst storms. A detailed study of the dynamics involved in a single storm is presented. It is shown that the relationship between VBs input and Dst output for this storm can be described in the context of the model of Burton et al. [1975> but with variable decay time and strength of coupling to the solar wind VBs parameter. During the storm recovery it is found that the decay time varies from ≈4 hours at the storm maximum to ≈20 hours midway in the recovery and then back to ≈10 hours. There appears to be nothing in the simultaneous solar wind data to explain this reversal in the evolution of the decay time. It is shown that the strength of coupling to the solar wind VBs parameter varies considerably. The coupling strength peaks strongly at the time of the storm maximum and decays to low values during the storm recovery. Solar wind VBs input during the storm recovery does not affect the recovery rate. Using this storm data, empirical nonlinear analogues are constructed. These analogues are tested out of sample for their prediction effectiveness. Comparisons with the predictions of the model due to Burton et al. are given. It is shown that these analogues are promising prediction tools, but their lack of sensitivity to solar wind dynamic pressure must be corrected. ¿ 1998 American Geophysical Union