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Many real-world time series exhibit multiple seasonality with different lengths. The removal of seasonal components is crucial in numerous applications of time series, including forecasting and anomaly detection. However, many…

Applications · Statistics 2021-09-21 Linxiao Yang , Qingsong Wen , Bo Yang , Liang Sun

The decomposition of a time series is an essential task that helps to understand its very nature. It facilitates the analysis and forecasting of complex time series expressing various hidden components such as the trend, seasonal…

Methodology · Statistics 2022-04-25 Grzegorz Dudek

We propose a new method for decomposing seasonal data: STR (a Seasonal-Trend decomposition using Regression). Unlike other decomposition methods, STR allows for multiple seasonal and cyclic components, covariates, seasonal patterns that may…

Methodology · Statistics 2021-07-02 Alexander Dokumentov , Rob J. Hyndman

Seasonal-trend decomposition is one of the most fundamental concepts in time series analysis that supports various downstream tasks, including time series anomaly detection and forecasting. However, existing decomposition methods rely on…

Machine Learning · Computer Science 2023-04-05 Xiao He , Ye Li , Jian Tan , Bin Wu , Feifei Li

Decomposing a complex time series into trend, seasonality, and remainder components is an important primitive that facilitates time series anomaly detection, change point detection, and forecasting. Although numerous batch algorithms are…

Machine Learning · Computer Science 2022-08-08 Abhinav Mishra , Ram Sriharsha , Sichen Zhong

The decomposition of time series into components is an important task that helps to understand time series and can enable better forecasting. Nowadays, with high sampling rates leading to high-frequency data (such as daily, hourly, or…

Applications · Statistics 2021-07-29 Kasun Bandara , Rob J Hyndman , Christoph Bergmeir

Time series forecasting presents significant challenges in real-world applications across various domains. Building upon the decomposition of the time series, we enhance the architecture of machine learning models for better multivariate…

Machine Learning · Computer Science 2026-02-24 Sanjeev Panta , Xu Yuan , Li Chen , Nian-Feng Tzeng

The monitoring and management of numerous and diverse time series data at Alibaba Group calls for an effective and scalable time series anomaly detection service. In this paper, we propose RobustTAD, a Robust Time series Anomaly Detection…

Machine Learning · Computer Science 2021-09-21 Jingkun Gao , Xiaomin Song , Qingsong Wen , Pichao Wang , Liang Sun , Huan Xu

Time series generation focuses on modeling the underlying data distribution and resampling to produce authentic time series data. Key components, such as trend and seasonality, drive temporal fluctuations, yet many existing approaches fail…

Machine Learning · Computer Science 2025-11-04 Zixuan Ma , Chenfeng Huang

Time series decomposition into trend, seasonal structure, and residual components is a core primitive for downstream analytics such as anomaly detection, change-point detection, and forecasting. However, most existing seasonal-trend…

Extracting the underlying trend signal is a crucial step to facilitate time series analysis like forecasting and anomaly detection. Besides noise signal, time series can contain not only outliers but also abrupt trend changes in real-world…

Machine Learning · Computer Science 2019-06-28 Qingsong Wen , Jingkun Gao , Xiaomin Song , Liang Sun , Jian Tan

The in-depth analysis of time series has gained a lot of research interest in recent years, with the identification of periodic patterns being one important aspect. Many of the methods for identifying periodic patterns require time series'…

Machine Learning · Computer Science 2019-11-15 Maximilian Toller , Roman Kern

Seasonal time series exhibit intricate long-term dependencies, posing a significant challenge for accurate future prediction. This paper introduces the Multi-scale Seasonal Decomposition Model (MSSD) for seasonal time-series forecasting.…

Machine Learning · Computer Science 2024-12-18 Yining Pang , Chenghan Li

Robust Anomaly Detection (AD) on time series data is a key component for monitoring many complex modern systems. These systems typically generate high-dimensional time series that can be highly noisy, seasonal, and inter-correlated. This…

Machine Learning · Computer Science 2020-07-29 Farzaneh Khoshnevisan , Zhewen Fan , Vitor R. Carvalho

Real-world systems are often complex, dynamic, and nonlinear. Understanding the dynamics of a system from its observed time series is key to the prediction and control of the system's behavior. While most existing techniques tacitly assume…

Computation · Statistics 2015-05-19 Bing Wang , Jie Sun , Adilson E. Motter

Time series forecasting is an important and forefront task in many real-world applications. However, most of time series forecasting techniques assume that the training data is clean without anomalies. This assumption is unrealistic since…

Machine Learning · Computer Science 2024-02-06 Hao Cheng , Qingsong Wen , Yang Liu , Liang Sun

Periodicity detection is an important task in time series analysis, but still a challenging problem due to the diverse characteristics of time series data like abrupt trend change, outlier, noise, and especially block missing data. In this…

Machine Learning · Computer Science 2023-03-08 Qingsong Wen , Linxiao Yang , Liang Sun

Multivariate time series in domains such as finance, climate science, and healthcare often exhibit long-term trends, seasonal patterns, and short-term fluctuations, complicating causal inference under non-stationarity and autocorrelation.…

Machine Learning · Computer Science 2026-04-29 Muhammad Hasan Ferdous , Md Osman Gani

We introduce BASTION (Bayesian Adaptive Seasonality and Trend DecompositION), a flexible Bayesian framework for decomposing time series into trend and multiple seasonality components. We cast the decomposition as a penalized nonparametric…

Methodology · Statistics 2026-01-27 Jason B. Cho , David S. Matteson

On-line detection of anomalies in time series is a key technique used in various event-sensitive scenarios such as robotic system monitoring, smart sensor networks and data center security. However, the increasing diversity of data sources…

Machine Learning · Computer Science 2021-04-26 Wentai Wu , Ligang He , Weiwei Lin , Yi Su , Yuhua Cui , Carsten Maple , Stephen Jarvis
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