Fast Online Changepoint Detection

TL;DR

This paper introduces a fast, online changepoint detection method for linear regression models that effectively detects early and late changes in various time series, with proven control over false alarms and quick detection times.

Contribution

It proposes a new class of weighted and composite CUSUM-based statistics for rapid changepoint detection applicable to diverse weakly dependent time series.

Findings

Controls Type I Error effectively

Achieves short detection delays

Works well across different time series

Abstract

We study online changepoint detection in the context of a linear regression model. We propose a class of heavily weighted statistics based on the CUSUM process of the regression residuals, which are specifically designed to ensure timely detection of breaks occurring early on during the monitoring horizon. We subsequently propose a class of composite statistics, constructed using different weighing schemes; the decision rule to mark a changepoint is based on the largest statistic across the various weights, thus effectively working like a veto-based voting mechanism, which ensures fast detection irrespective of the location of the changepoint. Our theory is derived under a very general form of weak dependence, thus being able to apply our tests to virtually all time series encountered in economics, medicine, and other applied sciences. Monte Carlo simulations show that our methodologies are able to control the procedure-wise Type I Error, and have short detection delays in the presence of breaks.