# RobustSTL: A Robust Seasonal-Trend Decomposition Algorithm for Long Time Series

arXiv: https://arxiv.org/abs/1812.01767 · HTML: https://mlsanity.com/paper/1812.01767/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2018.

## Built on by (most cited first, 30 of 54)

- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [CoST: Contrastive Learning of Disentangled Seasonal-Trend Representations for Time Series Forecasting](https://mlsanity.com/paper/2202.01575/) (2022)
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- [TFAD: A Decomposition Time Series Anomaly Detection Architecture with Time-Frequency Analysis](https://mlsanity.com/paper/2210.09693/) (2022)
- [Calibrated One-class Classification for Unsupervised Time Series Anomaly Detection](https://mlsanity.com/paper/2207.12201/) (2022)
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- [CloudRCA: A Root Cause Analysis Framework for Cloud Computing Platforms](https://mlsanity.com/paper/2111.03753/) (2021)
- [SSMF: Shifting Seasonal Matrix Factorization](https://mlsanity.com/paper/2110.12763/) (2021)
- [Unsupervised Deep Learning for IoT Time Series](https://mlsanity.com/paper/2302.03284/) (2023)
- [OneShotSTL: One-Shot Seasonal-Trend Decomposition For Online Time Series Anomaly Detection And Forecasting](https://mlsanity.com/paper/2304.01506/) (2023)
- [BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition](https://mlsanity.com/paper/2308.14906/) (2023)
- [A Multi-Scale Decomposition MLP-Mixer for Time Series Analysis](https://mlsanity.com/paper/2310.11959/) (2023)
- [A Systematic Review for Transformer-based Long-term Series Forecasting](https://mlsanity.com/paper/2310.20218/) (2023)
- [Time Series Analysis in Frequency Domain: A Survey of Open Challenges, Opportunities and Benchmarks](https://mlsanity.com/paper/2504.07099/) (2025)
- [AHPA: Adaptive Horizontal Pod Autoscaling Systems on Alibaba Cloud Container Service for Kubernetes](https://mlsanity.com/paper/2303.03640/) (2023)
- [Data Augmentation for Time-Series Classification: An Extensive Empirical Study and Comprehensive Survey](https://mlsanity.com/paper/2310.10060/) (2023)
- [Novel Physics-Based Machine-Learning Models for Indoor Air Quality Approximations](https://mlsanity.com/paper/2308.01438/) (2023)
- [E2USD: Efficient-yet-effective Unsupervised State Detection for Multivariate Time Series](https://mlsanity.com/paper/2402.14041/) (2024)
- [OnlineSTL: Scaling Time Series Decomposition by 100x](https://mlsanity.com/paper/2107.09110/) (2021)
- [GraphAD: A Graph Neural Network for Entity-Wise Multivariate Time-Series Anomaly Detection](https://mlsanity.com/paper/2205.11139/) (2022)
- [Improving Time Series Encoding with Noise-Aware Self-Supervised Learning and an Efficient Encoder](https://mlsanity.com/paper/2306.06579/) (2023)
- [Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties](https://mlsanity.com/paper/2106.06033/) (2021)
- [A Robust and Efficient Multi-Scale Seasonal-Trend Decomposition](https://mlsanity.com/paper/2109.08800/) (2021)
- [A Temporally Disentangled Contrastive Diffusion Model for Spatiotemporal Imputation](https://mlsanity.com/paper/2402.11558/) (2024)
- [AA-Forecast: Anomaly-Aware Forecast for Extreme Events](https://mlsanity.com/paper/2208.09933/) (2022)
- [Robust Dominant Periodicity Detection for Time Series with Missing Data](https://mlsanity.com/paper/2303.03553/) (2023)
- [Raising the ClaSS of Streaming Time Series Segmentation](https://mlsanity.com/paper/2310.20431/) (2023)
- [Data Augmentation for Multivariate Time Series Classification: An Experimental Study](https://mlsanity.com/paper/2406.06518/) (2024)

## Abstract (arXiv)

Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time series characteristics exhibiting in real-world data which are not addressed properly, including 1) ability to handle seasonality fluctuation and shift, and abrupt change in trend and reminder; 2) robustness on data with anomalies; 3) applicability on time series with long seasonality period. In the paper, we propose a novel and generic time series decomposition algorithm to address these challenges. Specifically, we extract the trend component robustly by solving a regression problem using the least absolute deviations loss with sparse regularization. Based on the extracted trend, we apply the the non-local seasonal filtering to extract the seasonality component. This process is repeated until accurate decomposition is obtained. Experiments on different synthetic and real-world time series datasets demonstrate that our method outperforms existing solutions.