  Time series anomaly detection is challenging due to the complexity and
variety of patterns that can occur. One major difficulty arises from modeling
time-dependent relationships to find contextual anomalies while maintaining
detection accuracy for point anomalies. In this paper, we propose a framework
for unsupervised time series anomaly detection that utilizes point-based and
sequence-based reconstruction models. The point-based model attempts to
quantify point anomalies, and the sequence-based model attempts to quantify
both point and contextual anomalies. Under the formulation that the observed
time point is a two-stage deviated value from a nominal time point, we
introduce a nominality score calculated from the ratio of a combined value of
the reconstruction errors. We derive an induced anomaly score by further
integrating the nominality score and anomaly score, then theoretically prove
the superiority of the induced anomaly score over the original anomaly score
under certain conditions. Extensive studies conducted on several public
datasets show that the proposed framework outperforms most state-of-the-art
baselines for time series anomaly detection.
