Recent technological advances provide researchers with a way of gathering real-time information on an individual's movement through the use of wearable devices that record acceleration. In this paper, we propose a method for identifying activity types, like walking, standing, and resting, from acceleration data. Our approach decomposes movements into short components called "movelets", and builds a reference for each activity type. Unknown activities are predicted by matching new movelets to the reference. We apply our method to data collected from a single, three-axis accelerometer and focus on activities of interest in studying physical function in elderly populations. An important technical advantage of our methods is that they allow identification of short activities, such as taking two or three steps and then stopping, as well as low frequency rare(compared with the whole time series) activities, such as sitting on a chair. Based on our results we provide simple and actionable recommendations for the design and implementation of large epidemiological studies that could collect accelerometry data for the purpose of predicting the time series of activities and connecting it to health outcomes.