A major goal of neuroscience is to identify general principles that can explain the diverse structures and functions of the brain. The principle of temporal prediction provides one approach, arguing that the sensory brain is optimized to represent stimulus features that efficiently predict the immediate future input. Previous work has demonstrated that feedforward hierarchical temporal prediction models can capture the tuning properties of neurons along the visual pathway, and that recurrent temporal prediction models can explain local functional connectivity within primary visual cortex. However, the visual system is also characterized by extensive inter-areal feedback recurrency, which existing models lack. We aimed to better account for the dynamic features of neurons in the visual cortex by incorporating both local recurrency and inter-areal feedback connectivity into a hierarchical temporal prediction model. The resulting model captured tuning properties along the dorsal visual pathway, including pattern motion selectivity and surround suppression, and the contribution of inter-areal connectivity to these properties. Moreover, compared with several alternative normative models, the hierarchical recurrent temporal prediction model provided the closest fit to these tuning properties and was best able to explain neuronal responses to natural stimuli. Accordingly, temporal prediction accounts well for information processing along the visual pathway.