The autocorrelation and power spectral density functions of a total of 14 strong-motion accelerograms of the Parkfield earthquake are obtained. When the ground motions are treated as random phenomena, these functions are found appropriate to be used as statistical characterization functions for the ground motions. Spectral simulation procedure is employed to determine the modal contributions of the motion and the ground characteristic damping and frequency at each station. The results can be used to construct reasonable single- or two-degree-of-freedom linear filters for the generation of a stationary stochastic model for the ground motion. The implications and engineering significance of the basic results are also discussed in some detail.