We develop a class of models for processes indexed in time and space that are based on autoregressive (AR) processes at each location. We use a Bayesian hierarchical structure to impose spatial coherence for the coefficients of the AR processes. The priors on such coefficients consist of spatial processes that guarantee time stationarity at each point in the spatial domain. The AR structures are coupled with a dynamic model for the mean of the process, which is expressed as a linear combination of time-varying parameters. We use satellite data on sea surface temperature for the North Pacific to illustrate how the model can be used to separate trends, cycles, and short-term variability for high-frequency environmental data. This article has supplementary material online.