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

翻译：本文提出BASTION（贝叶斯自适应季节性与趋势分解框架），这是一种灵活的贝叶斯框架，用于将时间序列分解为趋势分量与多重季节性分量。我们将该分解问题构建为惩罚非参数回归模型，并建立了趋势分量与季节性分量可唯一识别的形式化条件——该问题在现有文献中仅被非正式地讨论。相较于现有分解方法，BASTION具备三大关键优势：（1）在突变情况下仍能准确估计趋势与季节性；（2）对异常值和时变波动性具有更强的鲁棒性；（3）提供稳健的不确定性量化。我们通过模拟数据集和真实世界数据集，将BASTION与TBATS、STR及MSTL等经典方法进行了对比评估。BASTION能够有效捕捉复杂动态特征，同时兼顾异常值与异方差性等不规则分量，从而提供更精细且可解释的分解结果。为支持后续研究与实践应用，BASTION已封装为R软件包发布于https://github.com/Jasoncho0914/BASTION。