Epidemic changepoint detection in the presence of nuisance changes

Abstract: Many time series problems feature epidemic changes - segments where a parameter deviates from a background baseline. The number and location of such changes can be estimated in a principled way by existing detection methods, providing that the background level is stable and known. However, practical data often contains nuisance changes in background level, which interfere with standard estimation techniques. Furthermore, such changes often differ from the target segments only in duration, and appear as false alarms in the detection results. To solve these issues, we propose a two-level detector that models and separates nuisance and signal changes. As part of this method, we developed a new, efficient approach to simultaneously estimate unknown, but fixed, background level and detect epidemic changes. The analytic and computational properties of the proposed methods are established, including consistency and convergence. We demonstrate via simulations that our two-level detector provides accurate estimation of changepoints under a nuisance process, while other state-of-the-art detectors fail. Using real-world genomic and demographic datasets, we demonstrate that our method can identify and localise target events while separating out seasonal variations and experimental artefacts.