Multiple change point detection under serial dependence: Wild contrast maximisation and gappy Schwarz algorithm

TL;DR

This paper introduces a new methodology for detecting multiple change points in the mean of autocorrelated linear time series, combining wild contrast maximisation and the gappy Schwarz algorithm for improved accuracy and model selection.

Contribution

It develops the WCM.gSa method that simultaneously estimates change points and dependence structure without needing to estimate noise level, with proven consistency and strong empirical performance.

Findings

WCM.gSa accurately detects change points in simulations.

The method effectively estimates dependence structure.

Application to air quality data demonstrates practical utility.

Abstract

We propose a methodology for detecting multiple change points in the mean of an otherwise stationary, autocorrelated, linear time series. It combines solution path generation based on the wild contrast maximisation principle, and an information criterion-based model selection strategy termed gappy Schwarz algorithm. The former is well-suited to separating shifts in the mean from fluctuations due to serial correlations, while the latter simultaneously estimates the dependence structure and the number of change points without performing the difficult task of estimating the level of the noise as quantified e.g.\ by the long-run variance. We provide modular investigation into their theoretical properties and show that the combined methodology, named WCM.gSa, achieves consistency in estimating both the total number and the locations of the change points. The good performance of WCM.gSa is demonstrated via extensive simulation studies, and we further illustrate its usefulness by applying the methodology to London air quality data.