[Paper Review] Multiple Changepoint Detection with Partial Information on Changepoint Times

Yingbo Li, Robert Lund+1 more|arXiv (Cornell University)|Nov 23, 2015

Statistical Methods and Inference46 references3 citations

TL;DR

This paper introduces a minimum description length (MDL) procedure for detecting multiple changepoints in time series when partial prior information—such as metadata on likely changepoint times or concurrent shifts in bivariate series—is available. By incorporating this information into a Bayesian MDL framework, the method achieves consistent estimation with optimal convergence rates and significantly improves detection power and accuracy, especially in climate data homogenization applications.

ABSTRACT

This paper proposes a new minimum description length procedure to detect multiple changepoints in time series data when some times are a priori thought more likely to be changepoints. This scenario arises with temperature time series homogenization pursuits, our focus here. Our Bayesian procedure constructs a natural prior distribution for the situation, and is shown to estimate the changepoint locations consistently, with an optimal convergence rate. Our methods substantially improve changepoint detection power when prior information is available. The methods are also tailored to bivariate data, allowing changes to occur in one or both component series.

Motivation & Objective

• To develop a changepoint detection method that incorporates partial prior information on changepoint locations, such as metadata from station history logs.
• To improve detection power and estimation accuracy in time series with correlated data, particularly in climate homogenization of temperature records.
• To extend the MDL framework to handle concurrent changes in bivariate time series, such as Tmax and Tmin, where shifts are more likely to occur simultaneously.
• To establish theoretical consistency and optimal convergence rates for changepoint estimation under infill asymptotics when prior information is used.
• To provide a practical, computationally feasible method that outperforms standard MDL and frequentist approaches when domain knowledge is available.

Proposed method

• Formulates a Bayesian MDL penalty that integrates prior knowledge about likely changepoint times using a natural prior distribution over changepoint configurations.
• Applies automatic penalty rules from information theory to assign different code lengths to bounded integers (changepoint locations), unbounded integers (number of changepoints), and real-valued parameters (mean shifts).
• Uses a bivariate extension of the MDL model to allow for concurrent changes in two component series, such as maximum and minimum temperature.
• Employs a least squares estimation framework for model parameters, ensuring asymptotic consistency of changepoint and mean shift estimators.
• Implements a model selection procedure that minimizes the total description length, balancing model fit and complexity while incorporating prior beliefs.
• Validates the method through simulations and real-world analysis of Tuscaloosa temperature data, using target-minus-reference series to enhance changepoint visibility.

Experimental results

Research questions

• RQ1 Can a minimum description length procedure be adapted to incorporate partial prior information on changepoint locations without sacrificing theoretical consistency?
• RQ2 How does the inclusion of metadata or concurrent shift assumptions improve changepoint detection power in correlated time series?
• RQ3 What is the theoretical convergence rate of the proposed MDL estimator under infill asymptotics when prior information is used?
• RQ4 How does the method perform in detecting artificial mean shifts in climate data when compared to standard MDL or frequentist approaches?
• RQ5 To what extent can the method detect outliers or data errors, such as typos in temperature records, through anomalous changepoint patterns?

Key findings

• The proposed Bayesian MDL method achieves consistent estimation of changepoint locations with an optimal convergence rate under infill asymptotics.
• Incorporating metadata or concurrent shift assumptions significantly improves detection power and estimation accuracy, especially in correlated time series like monthly temperature records.
• The method successfully detected 12 changepoints in the Tuscaloosa target-minus-reference temperature series, including known metadata events (e.g., 1956, 1987) and plausible outliers (e.g., 1938, 1946).
• The method flagged potential data errors, such as anomalous values in 1937 and 1938, which were later attributed to typos in the data record.
• The use of a composite reference series from three nearby stations helped mitigate spurious shifts from reference data, improving the reliability of changepoint detection.
• The model outperformed standard MDL and frequentist methods in detecting changepoints when prior information was available, particularly in bivariate settings with concurrent shifts.