Uncertainty-Aware Seasonal-Trend Decomposition Based on Loess

Area of Science:

• Time Series Analysis
• Statistical Modeling
• Data Visualization

Background:

• Seasonal-trend decomposition based on loess (STL) is a standard method for time series analysis.
• Existing STL methods do not adequately handle data with inherent uncertainty.
• Accurate decomposition and visualization of uncertain time series are crucial for reliable insights.

Purpose of the Study:

• To extend the STL method to effectively analyze and visualize time series data containing uncertainty.
• To develop a robust framework for propagating uncertainty through the decomposition process.
• To introduce novel visualization techniques for uncertain time series components.

Main Methods:

• Developed uncertainty-aware STL (UASTL) by mathematically propagating multivariate Gaussian distributions.
• Integrated Gaussian processes for modeling uncertainty in data, including uncertain areas and missing values.
• Designed advanced visualization techniques to address challenges in uncertainty and correlation display.

Main Results:

• UASTL precisely preserves stochastic quantities shared across decomposition components.
• The method enables STL-consistent sampling for time series visualization.
• Demonstrated effective exploration of correlations within and between decomposition components under uncertainty.
• Showcased analysis of the impact of varying uncertainty levels on time series decomposition.

Conclusions:

• UASTL provides a mathematically sound and effective extension of STL for uncertain time series.
• The developed visualization techniques significantly improve the interpretability of uncertain time series decompositions.
• UASTL offers a valuable tool for analyzing complex time series data with uncertainties, outperforming conventional STL in such scenarios.