2025/08/28 by Yiyin Zhang, Y. C. Zhang, Zhang, Yiyin +5 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Anomaly Detection Techniques and Applications #Complex Systems and Time Series Analysis #Constant (computer programming) #Point (geometry) #Polynomial #Relevance (law) #Remainder #Seasonality #Series (stratigraphy) #Time Series Analysis and Forecasting #Time series #math.ST #stat.AP #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.2508.21128
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Detecting anomalies in time series data is a challenging task with broad relevance in many applications. Existing methods work effectively only under idealized conditions, typically focusing on point anomalies or assuming a constant baseline. Our approach overcomes these limitations by detecting both collective and point anomalies, while allowing for polynomial trends and seasonal patterns. We establish statistical theory demonstrating that our method accurately decomposes the time series into anomaly, trend, seasonality, and remainder components. We further show that the approach provides a consistent estimate of the number of anomalies and their locations. Simulation studies confirm its strong detection performance with finite samples, and an application to energy price data illustrates its practical utility.