A widely held assumption within the field of Trajectory Prediction is the perfect and complete observation of agents’ pasts. While this assumption allows for a simpler representation of the prediction problem, it no longer holds true when prediction models are expected to operate on histories generated by upstream perception systems, which are susceptible to fail. Occlusions are a particularly important cause of perception failures. They fragment tracked agents’ trajectories, and can often hide their most recent position(s) from the perception system. While most prediction models that are currently being researched cannot account for the possible incompleteness of agents’ past histories, we devise a prediction model that is designed to directly operate on partially missing histories caused by occlusions. We present OcclusionFormer, a TransFormer based prediction model, which predicts agent’s futures from their last observed position, without requiring imputation of missing past positions. Experiments show that our design is occlusion capable, as it can predict from trajectories with partially missing data, while remaining performant in the ideal, fully observed scenario. We also conduct research on the integration of an occlusion map within our model, which could help narrow the region of plausible prediction for occluded agents. We observe that, while the addition of such a map does improve the coherence of predictions with respect to the configuration of the occluded space, it results in a degradation of prediction performance.