This paper concerns the spatial and intensity transformations that are required to adjust for the confounding effects of subject movement during functional MRI (fMRI) activation studies. An approach is presented that models, and removes, movement-related artifacts from fMRI time-series. This approach is predicated on the observation that movement-related effects are extant even after perfect realignment. Movement-related effects can be divided into those that are a function of position of the object in the frame of reference of the scanner and those that are due to movement in previous scans. This second component depends on the history of excitation experienced by spins in a small volume and consequent differences in local saturation. The spin excitation history thus will itself be a function of previous positions, suggesting an autoregression-moving average model for the effects of previous displacements on the current signal. A model is described as well as the adjustments for movement-related components that ensue. The empirical analyses suggest that (in extreme situations) over 90% of fMRI signal can be attributed to movement, and that this artifactual component can be successfully removed.