[Paper Review] Trend and Variance Adaptive Bayesian Changepoint Analysis & Local Outlier Scoring

Haoxuan Wu, David S. Matteson+1 more|arXiv (Cornell University)|Nov 18, 2020

Monetary Policy and Economic Impact42 references4 citations

TL;DR

This paper introduces Adaptive Bayesian Changepoints with Outliers (ABCO), a novel Bayesian state-space model that jointly detects changepoints and local outliers in time series with stochastic volatility. By integrating global-local shrinkage priors and threshold stochastic volatility, ABCO adaptively models trends, outliers, and heteroskedastic noise, outperforming existing methods in simulations and real-world applications involving complex, non-stationary data with significant outliers or variance shifts.

ABSTRACT

We adaptively estimate both changepoints and local outlier processes in a Bayesian dynamic linear model with global-local shrinkage priors in a novel model we call Adaptive Bayesian Changepoints with Outliers (ABCO). We utilize a state-space approach to identify a dynamic signal in the presence of outliers and measurement error with stochastic volatility. We find that global state equation parameters are inadequate for most real applications and we include local parameters to track noise at each time-step. This setup provides a flexible framework to detect unspecified changepoints in complex series, such as those with large interruptions in local trends, with robustness to outliers and heteroskedastic noise. Finally, we compare our algorithm against several alternatives to demonstrate its efficacy in diverse simulation scenarios and two empirical examples on the U.S. economy.

Motivation & Objective

• To develop a robust, adaptive Bayesian framework for detecting changepoints and local outliers in time series with complex, non-stationary behavior.
• To address the limitations of existing changepoint methods in handling outliers and heteroskedastic noise, which degrade performance in real-world applications.
• To extend Bayesian changepoint analysis by incorporating dynamic trend modeling with uncertainty quantification and outlier scoring.
• To enable model-based inference for structural breaks in interrupted time series, including effect size estimation at intervention points.
• To provide a flexible, interpretable alternative to black-box deep learning methods by combining shrinkage priors with state-space modeling.

Proposed method

• ABCO models each time series as a sum of three components: a locally varying trend, a sparse additive outlier signal, and a heteroskedastic noise process.
• The trend component uses a D-th order difference model with horseshoe-like shrinkage priors to promote sparsity and detect isolated changepoints.
• A threshold stochastic volatility process with Z-distributed innovations models time-varying volatility, enabling adaptive detection in high- and low-variance regions.
• Outliers are modeled using a horseshoe-plus prior to allow extreme values to be identified without distorting trend estimation.
• The state-space formulation enables efficient MCMC sampling for posterior inference, including credible intervals for trends and changepoint locations.
• The model is extended to interrupted time series by modeling the first difference of the trend at the intervention point, allowing posterior inference on effect size.

Experimental results

Research questions

• RQ1 Can a Bayesian state-space model jointly detect changepoints and local outliers while adapting to time-varying volatility?
• RQ2 How does the inclusion of local volatility tracking improve changepoint detection in non-homogeneous time series?
• RQ3 To what extent does ABCO outperform existing methods in the presence of significant outliers and stochastic volatility?
• RQ4 Can ABCO provide reliable uncertainty quantification for structural breaks in interrupted time series, including effect size estimation?
• RQ5 How does the use of global-local shrinkage priors enhance adaptivity in trend and changepoint estimation?

Key findings

• ABCO outperforms Fearnhead & Rigaill (2017) and Pein et al. (2017) in simulations with significant outliers and heteroskedastic noise, particularly in detecting true changepoints and minimizing false positives.
• The model successfully identifies a downward level shift in the rate of acute coronary events in Sicily after a smoking ban, with no evidence of slope change or temporary effects.
• Posterior inference on the first difference at the intervention time shows a mean shift of approximately -20, with substantial uncertainty, indicating a sustained but immediate effect.
• The model adapts to local volatility, showing increased uncertainty at the intervention point and maintaining stable inference in pre- and post-intervention periods.
• ABCO provides reliable 95% credible bands for both the trend and observation processes, demonstrating robust uncertainty quantification across time.
• The horseshoe-like shrinkage on trend differences effectively suppresses spurious fluctuations while allowing large, isolated changes to be detected as true changepoints.