BASTION: A Bayesian Framework for Trend and Seasonality Decomposition

2026-01-26

AI Summary

This work addresses the challenge of non-identifiability and sensitivity to structural breaks, outliers, and time-varying volatility in decomposing trend and multiple seasonal components from time series. The authors propose a Bayesian nonparametric regression framework that, through adaptive regularization and Markov chain Monte Carlo (MCMC) inference, establishes the first rigorous identifiability conditions for trend and multi-seasonal effects. This approach enables robust decomposition even in the presence of abrupt changes, anomalies, and heteroskedasticity, while delivering principled uncertainty quantification. Empirical evaluations on both synthetic and real-world datasets demonstrate superior performance over state-of-the-art methods such as TBATS, STR, and MSTL, yielding more accurate, interpretable, and reliable decompositions. An open-source R package implementing the method is made publicly available to the research community.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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 regression and establish formal conditions under which the trend and seasonal components are uniquely identifiable, an issue only treated informally in the existing literature. BASTION offers three key advantages over existing decomposition methods: (1) accurate estimation of trend and seasonality amidst abrupt changes, (2) enhanced robustness against outliers and time-varying volatility, and (3) robust uncertainty quantification. We evaluate BASTION against established methods, including TBATS, STR, and MSTL, using both simulated and real-world datasets. By effectively capturing complex dynamics while accounting for irregular components such as outliers and heteroskedasticity, BASTION delivers a more nuanced and interpretable decomposition. To support further research and practical applications, BASTION is available as an R package at https://github.com/Jasoncho0914/BASTION

Problem

• time series decomposition
• trend and seasonality
• identifiability
• outliers
• heteroskedasticity

Innovation

• Bayesian decomposition
• trend-seasonality identifiability
• nonparametric regression
• robust time series analysis
• uncertainty quantification