Hierarchical predictive coding is an influential model of cortical organization, in which sequential hierarchical layers are connected by feedback connections carrying predictions, as well as feedforward connections carrying prediction errors. To date, however, predictive coding models have neglected to take into account that neural transmission itself takes time. For a time-varying stimulus, such as a moving object, this means that feedback predictions become misaligned with new sensory input. We present an extended model implementing both feed-forward and feedback extrapolation mechanisms that realigns feedback predictions to minimize prediction error. This realignment has the consequence that neural representations across all hierarchical stages 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 motionposition illusions, and that it provides a solution to the temporal binding problem.