Trend and Variance Adaptive Bayesian Changepoint Analysis and Local Outlier Scoring

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 use 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 heteroscedastic 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.

Keywords:

• Anomaly detection
• Dynamic linear model
• Stochastic volatility
• Structural change
• Trend filtering

Acknowledgments

We would like to thank the editor and the referees for their thoughtful feedback and recommendations for helping improve the article. The authors would like to thank Dr. Michael Jauch, Post-Doctoral Associate at Cornell Center for Applied Mathematics, for his detailed feedback on early drafts of this article.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

Financial support is gratefully acknowledged from a Xerox PARC Faculty Research Award, National Science Foundation Awards 1455172, 1934985, 1940124, 1940276 and 2114143, USAID, and Cornell University Atkinson Center for a Sustainable Future.