BASTION: A Bayesian Framework for Trend and Seasonality Decomposition

Jason B. Cho, David S. Matteson
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:4627-4635, 2026.

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 \url{https://github.com/Jasoncho0914/BASTION}

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-cho26a, title = { BASTION: A Bayesian Framework for Trend and Seasonality Decomposition }, author = {Cho, Jason B. and Matteson, David S.}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {4627--4635}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/cho26a/cho26a.pdf}, url = {https://proceedings.mlr.press/v300/cho26a.html}, 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 \url{https://github.com/Jasoncho0914/BASTION} } }
Endnote
%0 Conference Paper %T BASTION: A Bayesian Framework for Trend and Seasonality Decomposition %A Jason B. Cho %A David S. Matteson %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-cho26a %I PMLR %P 4627--4635 %U https://proceedings.mlr.press/v300/cho26a.html %V 300 %X 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 \url{https://github.com/Jasoncho0914/BASTION}
APA
Cho, J.B. & Matteson, D.S.. (2026). BASTION: A Bayesian Framework for Trend and Seasonality Decomposition . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:4627-4635 Available from https://proceedings.mlr.press/v300/cho26a.html.

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