Identifying patterns in time series that exhibit anomalous behavior is of increasing importance in many domains, such as financial and Web data analysis. In real applications, time series data often arrive continuously, and usually only a single scan is allowed through the data. Batch learning and retrospective segmentation methods would not be well applicable to such scenarios. In this paper, we present an online nonparametric Bayesian method OLAD for anomaly analysis in streaming time series. Moreover, we develop a novel and efficient online learning approach for the OLAD model based on stochastic gradient descent. The proposed method can effectively learn the underlying dynamics of anomaly-contaminated heavy-tailed time series and identify potential anomalous events. Empirical analysis on real-world datasets demonstrates the effectiveness of our method.