For performance‐based design, nonlinear dynamic structural analysis using various types of input ground motions is required. Stochastic (simulated) ground motions are sometimes useful as input motions, because their properties can be varied systematically to study the impact of ground‐motion properties on structural response, and producing large numbers of ground motions is simple. This paper describes an approach by which the wavelet packet transform can be used to characterize complex time‐varying earthquake ground motions, and it illustrates the potential benefits of such an approach in a variety of earthquake engineering applications. A model is developed that requires 13 parameters to describe a given ground motion. These 13 parameters are then related to seismological variables such as earthquake magnitude, distance, and site condition, through regression analysis that captures trends in mean values, standard deviations, and correlations of these parameters observed in recorded strong ground motions from 25 past earthquakes. The resulting regression equations can then be used to predict ground motions for a future earthquake scenario. This model is analogous to widely used empirical ground‐motion prediction equations (formerly called attenuation models) except that this model predicts entire time series rather than only response spectra. The ground motions produced using this predictive model are explored in detail, and have elastic response spectra, inelastic response spectra, durations, mean periods, and so forth, that are consistent in both mean and variability with existing published predictive models for those properties.