Each of the modeling extensions is illustrated with case studies, either in behavioral science, criminology, air pollution, or water resource settings. The multi-consequence intervention modeling procedure is developed based on the univariate Autoregressive Moving Average (ARMA) model to allow for a description of a change in mean level and covariance in a process due to an intervention. A system containing more than one location is described, where the intervention program is assumed to be initiated at any chosen location. Nonequal difference preference systems are considered, and the component of the STARMA model to be modified to describe diffusion preference is examined in scaled weight matrices. Two approaches, the strip region approach and the angular region approach, are proposed to construct the nonequally preferential neighbor structure that reflects the nonequally preferential diffusion process. A spatial model containing only contemporaneous terms is introduced, and the coupling and reparameterizing of the aggregate purely spatial model and the space-time model are analyzed. The coupled and reparameterized models may be dependent on or independent of the modeling sequence; the systems that give rise to each are distinguished, and the appropriate modeling procedures are described. The development of modeling procedures for the ergodic process is also discussed. Fifty tables, 88 figures, and 25 references are given.