Predicting the motion of other agents in a scene is highly relevant for autonomous driving, as it allows a self-driving car to anticipate. Inspired by the success of decoder-only models for language modeling, we propose DONUT, a Decoder-Only Network for Unrolling Trajectories. Different from existing encoder-decoder forecasting models, we encode historical trajectories and predict future trajectories with a single autoregressive model. This allows the model to make iterative predictions in a consistent manner, and ensures that the model is always provided with up-to-date information, enhancing the performance. Furthermore, inspired by multi-token prediction for language modeling, we introduce an 'overprediction' strategy that gives the network the auxiliary task of predicting trajectories at longer temporal horizons. This allows the model to better anticipate the future, and further improves the performance. With experiments, we demonstrate that our decoder-only approach outperforms the encoder-decoder baseline, and achieves new state-of-the-art results on the Argoverse 2 single-agent motion forecasting benchmark.