RobustSTL: A Robust Seasonal-Trend Decomposition Algorithm for Long Time Series (1812.01767v1)

Abstract: 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.

• The paper introduces RobustSTL, a novel algorithm that robustly extracts trend and seasonal components from long time series data.
• The method leverages LAD regression with sparse regularization and non-local seasonal filtering to effectively handle anomalies and abrupt shifts.
• Empirical tests show lower MSE and MAE compared to traditional methods, enhancing anomaly detection and forecasting capabilities.

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

RobustSTL is presented as a novel approach to the seasonal-trend decomposition of long time series data, addressing critical gaps identified in previous methods. The primary concerns addressed involve the handling of fluctuation and shift in seasonality, abrupt changes in trend, robustness against anomalies, and applicability to time series with long seasonality periods. This paper delineates the development and evaluation of the RobustSTL algorithm, proposing it as a significant improvement over existing methodologies.

Methodological Overview

The authors introduce a decomposition method that leverages least absolute deviations (LAD) regression paired with sparse regularization to extract trend components robustly. This technique inherently favors robustness against outliers, which is critical for handling real-world data with inherent noise and anomalies. Furthermore, non-local seasonal filtering is employed to distill the seasonal component effectively, allowing the process to accommodate shifts and fluctuations in seasonality that challenge traditional methods.

The work distinguishes itself by its iterative approach to decomposition, which continuously refines the trend and seasonality components until a satisfactory level of accuracy is achieved. This iterative refinement embodies the adaptability needed when dealing with extended time series, often prevalent in IoT applications where seasonal periods can be conceptually as long as a day, or even more extended depending on the data collection frequency.

Result Highlights

In empirical validations, RobustSTL outperforms existing approaches on both synthetic and real-world datasets. When assessing the method’s efficacy in decomposition, it demonstrates superior precision in capturing abrupt changes in the trend and accommodating seasonality shifts. Quantitative metrics such as mean squared error (MSE) and mean absolute error (MAE) substantiate these claims, showcasing lower values compared to STL, TBATS, and STR methods. This indicates that RobustSTL is more adept at recovering underlying signals and segregating anomalies.

Implications and Future Directions

The practical implications of RobustSTL are manifold, particularly in fields such as anomaly detection and forecasting. The enhanced decomposition technique allows for more robust identification of anomalies, a critical aspect in sectors like finance, healthcare, and industrial systems where early detection can lead to significant operational efficiencies and risk mitigation.

Theoretically, the approach posits advancements in the modeling of time series data, highlighting the potential for integration with higher-level analytical procedures, such as embedding decomposition strategies directly into anomaly detection frameworks. Future research could explore these integrations, refining predictive models by leveraging decomposed components as intrinsic predictive variables.

RobustSTL signifies a noteworthy advancement in time series analysis, providing a method that is both conceptually robust and computationally efficient. As data volumes continue to expand and the need for accurate forecasts intensifies, strategies like RobustSTL offer a promising avenue for managing complexity in time series data, enabling more nuanced understandings and applications across diverse domains.