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Falls on the stairs are a common cause of accidental injury among the older adults. Understanding the mechanisms leading to such accidents may improve not only the prevention of falls, but also support independent living among elderly. Thus, a method to automatically detect falls and other abnormal events on stairs is presented and empirically validated. Automatic fall detection will also assist in data collection for environmental design improvements and fall prevention. Real-time 3D joint tracking information, provided by a Microsoft Kinect, is used to estimate the walking speed and to extract a set of features that encode human motion during stairway descent. Supervised learning algorithms, trained on manually labelled training data simulated in a home laboratory, obtained a high detection accuracy rate of ~92% in leave-one-subject-out cross validation. In contrast with previous research, which identified visual tracking of the feet as the best indicator of dangerous activity, 3D motion of the hips is experimentally shown to be the most informative component in detecting abnormal events in the 3D tracking data provided by the Kinect.