The nonlinear dynamical models of the coupled solar wind-magnetosphere system derived from observational data have been used to yield efficient forecasts of the magnetospheric conditions. These data-derived models have the advantage of capturing the essential features inherent in the data and thus can be improved as larger and better databases become available. Current models are based largely on the data of periods when the magnetosphere is weakly driven. For example, the widely used Bargatze et al. (1985) data set corresponds to a declining phase of the solar cycle and contains only a few weak storms. A correlated database of solar wind and magnetospheric time series data for the last solar cycle near its peak (year 2001) is compiled and used to model the magnetospheric dynamics under strong driving. The solar wind variables are obtained from ACE spacecraft, while the magnetospheric response consists of geomagnetic indices as well as magnetic perturbations measured by ground magnetometers. The dynamical models of the magnetosphere during superstorms developed with this database are used to forecast the geospace storms of October--November 2003 and April 2002 and yields improved forecasts of the intense storms. A new technique is introduced for data-derived modeling based on the distances of the nearest neighbors from the current state. In this technique the contributions of the nearest neighbors are weighted by factors inversely proportional to the distances in the reconstructed phase space. This yields better predictions, especially during the strongly driven periods. The comparison of the models based on the year 2001 and Bargatze et al. (1985) databases show the similarities and differences in the magnetospheric states during solar maximum and minimum periods.