Periodic transitions from place to place are inherent in human movements. Through visual examination we detect these periodic movements in traces of user tracking data. However such user tracking data sets tend to be sparse and incomplete. In addition, periodic movements are surrounded by noise: transitions to and from less frequently visited places and transitions to one of a kind visits. In this paper, we present algorithms leveraging techniques and models to detect periodicity in individual user movements. Our algorithms predict a user's next place given only the current context of timestamp and location. We apply these algorithms to real user mobility data sets. Prediction accuracy depends on the ratio of periodic movements to noise in user traces. For majority of users in a movement tracking data set collected over a year, our algorithms achieve next place prediction accuracies of 50% and above.