BASTION: A Bayesian Framework for Trend and Seasonality Decomposition

TL;DR

BASTION is a Bayesian framework that accurately decomposes time series into trend and multiple seasonal components, robustly handling outliers and volatility, with formal identifiability guarantees and practical implementation as an R package.

Contribution

It introduces a novel Bayesian approach for time series decomposition with formal identifiability conditions and improved robustness over existing methods.

Findings

Outperforms TBATS, STR, and MSTL in simulations and real data.

Effectively captures complex dynamics and irregular components.

Provides reliable uncertainty quantification.

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