The rodent head direction (HD) system, which codes for the animal's head direction in the horizontal plane, is thought to be critically involved in spatial navigation. Electrophysiological recording studies have shown that HD cells can anticipate the animal's HD by up to 75-80 ms. The origin of this anticipation is poorly understood. In this modeling study we provide a novel explanation for HD anticipation, which relies on the firing properties of neurons afferent to the HD system. By incorporating spike rate adaptation and post-inhibitory rebound as observed in medial vestibular nucleus neurons, our model produces realistic anticipation on a large corpus of rat movement data. In addition, HD anticipation varies significantly between recording sessions of the same cell, between active and passive movement, and between different studies. Such differences do not appear to be correlated with behavioral variables, and cannot be accounted for using earlier models. In the present model, anticipation depends on the power spectrum of the head movements. By direct comparison with recording data, we show that the model explains 60% to 80% of the observed anticipation variability. We conclude that HD afferent dynamics and the statistics of rat head movements are important in generating HD anticipation. This result contributes to understanding the functional circuitry of the HD system and has methodological implications for studies of HD anticipation.