Methods for event time series prediction and anomaly detection

Event time series are sequences of events occurring in continuous time. They arise in many real-world problems and may represent, for example, posts in social media, administrations of medications to patients, or adverse events, such as episodes of atrial fibrillation or earthquakes. In this work, we study and develop methods for prediction and anomaly detection on event time series. We study two general approaches. The first approach converts event time series to regular time series of counts via time discretization. We develop methods relying on (a) nonparametric time series decomposition and (b) dynamic linear models for regular time series. The second approach models the events in continuous time directly. We develop methods relying on point processes. For prediction, we develop a new model based on point processes to combine the advantages of existing models. It is flexible enough to capture complex dependency structures between events, while not sacrificing applicability in common scenarios. For anomaly detection, we develop methods that can detect new types of anomalies in continuous time and that show advantages compared to time discretization