Epidemic Change Detection via Shifted Maximum Subarrays

Abstract

The epidemic change-point problem arises in applications where a sequence exhibits a temporary deviation in its mean over an unknown interval. Classical approaches are based on the scan statistic, which requires maximizing a normalized sample mean over all possible segments. As a result, exact computation of the scan statistic involves $O(n^2)$ operations for a sequence of length $n$, which greatly limits its applicability to large datasets.In this work, we introduce a new computational framework based on the shifted maximum subarray (SMS) problem. We establish that the scan statistic can be derived from the SMS solution path, thereby transforming a quadratic-time optimization into an empirically near-linear-time procedure. This result provides an exact and scalable algorithm for computing scan statistics without approximation. We further develop permutation-based and hybrid inference methods that enable efficient and reliable significance calibration. The proposed approach achieves accurate type I error control and competitive power, as demonstrated through simulations and real data analyses.