Testing for a Change in Mean After Changepoint Detection

TL;DR

This paper introduces a new statistical framework for testing the null hypothesis of no change in mean after changepoint detection, applicable to various estimation methods, and demonstrates its effectiveness through simulations and real data analysis.

Contribution

It proposes a novel framework for post-detection mean change testing that requires less information, increasing test power, and is compatible with multiple changepoint estimation techniques.

Findings

Higher power tests due to less conditioning.

Applicable to binary segmentation, $\, ext{l}_0$ segmentation, and fused lasso.

Validated through simulations and chromosomal data analysis.

Abstract

While many methods are available to detect structural changes in a time series, few procedures are available to quantify the uncertainty of these estimates post-detection. In this work, we fill this gap by proposing a new framework to test the null hypothesis that there is no change in mean around an estimated changepoint. We further show that it is possible to efficiently carry out this framework in the case of changepoints estimated by binary segmentation and its variants, $\ell_{0}$ segmentation, or the fused lasso. Our setup allows us to condition on much less information than existing approaches, which yields higher powered tests. We apply our proposals in a simulation study and on a dataset of chromosomal guanine-cytosine content. These approaches are freely available in the R package ChangepointInference at https://jewellsean.github.io/changepoint-inference/.