Hierarchical predictive coding is an influential model of cortical organization, in which sequential hierarchical levels are connected by backward connections carrying predictions, as well as forward connections carrying prediction errors. To date, however, predictive coding models have largely neglected to take into account that neural transmission itself takes time. For a time-varying stimulus, such as a moving object, this means that backward predictions become misaligned with new sensory input. We present an extended model implementing both forward and backward extrapolation mechanisms that realigns backward predictions to minimize prediction error. This realignment has the consequence that neural representations across all hierarchical levels become aligned in real time. Using visual motion as an example, we show that the model is neurally plausible, that it is consistent with evidence of extrapolation mechanisms throughout the visual hierarchy, that it predicts several known motion–position illusions in human observers, and that it provides a solution to the temporal binding problem.