The ability to accurately and consistently discover anomalies in time series is important in many applications. Fields such as finance (fraud detection), information security (intrusion detection), healthcare, and others all benefit from anomaly detection. Intuitively, anomalies in time series are time points or sequences of time points that deviate from normal behavior characterized by periodic oscillations and long-term trends. For example, the typical activity on e-commerce websites exhibits weekly periodicity and grows steadily before holidays. Similarly, domestic usage of electricity exhibits daily and weekly oscillations combined with long-term season-dependent trends. How can we accurately detect anomalies in such domains while simultaneously learning a model for normal behavior? We propose a robust offline unsupervised framework for anomaly detection in seasonal multivariate time series, called AURORA. A key innovation in our framework is a general background behavior model that unifies periodicity and long-term trends. To this end, we leverage a Ramanujan periodic dictionary and a spline-based dictionary to capture both seasonal and trend patterns. We conduct experiments on both synthetic and real-world datasets and demonstrate the effectiveness of our method. AURORA has significant advantages over existing models for anomaly detection, including high accuracy (AUC of up to 0.98), interpretability of recovered normal behavior (\(100\%\) accuracy in period detection), and the ability to detect both point and contextual anomalies. In addition, AURORA is orders of magnitude faster than baselines.

在许多应用中，准确一致地发现时间序列异常的能力很重要。金融（欺诈检测）、信息安全（入侵检测）、医疗保健等领域都受益于异常检测。直观地说，时间序列中的异常是偏离以周期性振荡和长期趋势为特征的正常行为的时间点或时间点序列。例如，电子商务网站上的典型活动呈现出每周周期性，并在节前稳步增长。同样，家庭用电表现出每日和每周的波动，以及长期的季节性趋势。我们如何在学习正常行为模型的同时准确检测这些领域的异常情况？我们提出了一个强大的离线无监督框架，用于季节性多元时间序列中的异常检测，称为 AURORA。我们框架中的一项关键创新是统一了周期性和长期趋势的通用背景行为模型。为此，我们利用 Ramanujan 周期性字典和基于样条的字典来捕获季节性和趋势模式。我们对合成数据集和真实数据集进行实验，并证明我们方法的有效性。与现有的异常检测模型相比，AURORA 具有显着优势，包括高精度（AUC 高达 0.98）、恢复正常行为的可解释性（\(100\%\)周期检测的准确性），以及检测点和上下文异常的能力。此外，AURORA 比基线快几个数量级。