Testing for a Change in Mean After Changepoint Detection

Jewell, Sean and Fearnhead, Paul and Witten, Daniela (2022) Testing for a Change in Mean After Changepoint Detection. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 84 (4). pp. 1082-1104. ISSN 1369-7412

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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, (Formula presented.) 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/.