Recognizing abnormal events such as traffic violations and accidents in natural driving scenes is essential for successful autonomous driving and advanced driver assistance systems. However, most work on video anomaly detection suffers from two crucial drawbacks. First, they assume cameras are fixed and videos have static backgrounds, which is reasonable for surveillance applications but not for vehicle-mounted cameras. Second, they pose the problem as one-class classification, relying on arduously hand-labeled training datasets that limit recognition to anomaly categories that have been explicitly trained. This paper proposes an unsupervised approach for traffic accident detection in first-person (dashboard-mounted camera) videos. Our major novelty is to detect anomalies by predicting the future locations of traffic participants and then monitoring the prediction accuracy and consistency metrics with three different strategies. We evaluate our approach using a new dataset of diverse traffic accidents, AnAn Accident Detection (A3D), as well as another publicly-available dataset. Experimental results show that our approach outperforms the state-of-the-art.