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A commonly-used representation for motion prediction of actors is a sequence of waypoints (comprising positions and orientations) for each actor at discrete future time-points. While this approach is simple and flexible, it can exhibit unrealistic higher-order derivatives (such as acceleration) and approximation errors at intermediate time steps. To address this issue we propose a simple and general representation for temporally continuous probabilistic trajectory prediction that is based on polynomial trajectory parameterization. We evaluate the proposed representation on supervised trajectory prediction tasks using two large self-driving data sets. The results show realistic higher-order derivatives and better accuracy at interpolated time-points, as well as the benefits of the inferred noise distributions over the trajectories. Extensive experimental studies based on existing state-of-the-art models demonstrate the effectiveness of the proposed approach relative to other representations in predicting the future motions of vehicle, bicyclist, and pedestrian traffic actors.