A vast amount of temporal information are collected and stored which leads to a need for techniques to extract useful high-level information from the data, such as recognizable activities or events. This paper proposes a framework for streaming analysis of time series data, in this case track data from video sequences, which can recognize events without supervision and memorize them by building temporal contexts. The memorized historical data are then used to predict the future and detect anomalous activities or events. An incremental clustering method is used to recognize and learn the event without training. A memorization method of double localization, including relative and absolute localization, is proposed to model the temporal context. The first- order Markov chain is used as an example to relatively localize an event in the temporal space, while a temporal map is used to absolutely localize an event. By setting proper coordinates for the temporal map, prior temporal patterns can be included before building more delicate models to find subtle patterns. Finally, the predictive model is built based on the method of memorization. The "Edinburgh Informatics Forum Pedestrian Data Set", which offers about 1000 observed trajectories of pedestrians detected in camera images each working day for several months, is used as an example to illustrate the framework. The trajectories are incrementally recognized as activities, and the activities are further used to describe the situation (event) in the scene. By using the proposed framework, we not only get current high level information of the scene, such as activities and events that occur in the scene, but we can also reason whether current activities or events are "normal" by referring to the temporal context learned from historical data. For the data considered here, a total of 92,000+ observed trajectories and their temporal patterns over one year can be summarized by a temporal map of 16 events and a probability (transition) matrix between them. Our proposed framework offers an effective method of extracting useful and manageable information from a huge amount of raw trajectory data.