The magnetospheric dynamics consists of global and multiscale components. The local-linear filters (LLFs) relating the solar wind input and the magnetospheric output have been used earlier to predict the global dynamical behavior. In this paper, the relative role of global and multiscale processes in the prediction of magnetospheric dynamics is studied. The filters are derived from the reconstructed input--output magnetospheric phase space using time series of VBS as the input and AL index as the output. We show that the conventional formula for the LLF can be broken into two parts corresponding to the global and multiscale constituents. The first part is the zeroth-order term, which is obtained by the phase space average of the model outputs. This is a feature similar to the mean-field model in phase transition physics, which yields iterative predictions of the global coherent component. The second part consists of the higher-order terms of the filter, which are highly irregular and thus cannot be used in dynamical prediction. This irregular behavior represents the departure from the low-dimensional dynamics underlying earlier studies using LLFs. The earlier prediction studies mixed these two components. However, by separating these two components, the prediction procedure is highly simplified and longer period predictions are achieved. The multiscale nature arises from the perturbations over a wide range of scales and has a power spectrum similar to that of colored noise. When these perturbations are taken into account in the prediction process, the iterative predictions yield a factor of four improvement in the accuracy compared to the mean-field model. However, the filter technique does not provide a prescription for correctly including the multiscale aspects in a dynamical model and further improvement in forecasting can be achieved by a statistical approach. These results have important implications for space weather forecasting.