PROBABILISTIC SEASONAL-TREND DECOMPOSITION OF TIME SERIES USING LOCALLY WEIGHTED REGRESSION
Keywords:
Time series decomposition, probabilistic modeling, seasonal-trend analysis, locally weighted regressionAbstract
Time series decomposition is a fundamental technique for analyzing temporal data, enabling the separation of underlying patterns such as trend, seasonality, and remainder components. While robust decomposition methods like Seasonal-Trend Decomposition using Loess (STL) are widely employed, they typically do not account for or propagate inherent uncertainties present in the raw data or during the estimation process. This article introduces a novel framework for Probabilistic Seasonal-Trend Decomposition that explicitly incorporates uncertainty awareness, building upon the established Loess-based approach. We detail methodologies for quantifying and propagating uncertainty through each stage of the decomposition, providing not only point estimates for trend and seasonal components but also associated confidence intervals. Through hypothetical scenarios, we demonstrate how this uncertainty-aware decomposition can yield a more comprehensive and realistic understanding of time-varying phenomena, offering improved interpretability and more robust decision-making in diverse applications ranging from climate science to financial forecasting.
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Copyright (c) 2025 Prof. Henrik O. Bergstrom, Dr. Carla M. Oliveira
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