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The detection of abnormal moving objects over high-volume trajectory streams is critical for real-time applications ranging from military surveillance to transportation management. Yet this outlier detection problem, especially along both the spatial and temporal dimensions, remains largely unexplored. In this work, we propose a rich taxonomy of novel classes of neighbor-based trajectory outlier definitions that model the anomalous behavior of moving objects for a large range of real-time applications. Our theoretical analysis and empirical study on two real-world datasets—the Beijing Taxi trajectory data and the Ground Moving Target Indicator data stream—and one generated Moving Objects dataset demonstrate the effectiveness of our taxonomy in effectively capturing different types of abnormal moving objects. Furthermore, we propose a general strategy for efficiently detecting these new outlier classes called the minimal examination (MEX) framework. The MEX framework features three core optimization principles, which leverage spatiotemporal as well as the predictability properties of the neighbor evidence to minimize the detection costs. Based on this foundation, we design algorithms that detect the outliers based on these classes of new outlier semantics that successfully leverage our optimization principles. Our comprehensive experimental study demonstrates that our proposed MEX strategy drives the detection costs 100-fold down into the practical realm for applications that analyze high-volume trajectory streams in near real time.