TWIN: Two window inspection for online change point detection

Abstract

We propose a new class of sequential change point tests, both for changes in the mean parameter and in the overall distribution function. The methodology builds on a two-window inspection scheme (TWIN), which aggregates data into symmetric samples and applies strong weighting to enhance statistical performance. The detector yields logarithmic rather than polynomial detection delays, representing a substantial reduction compared to state-of-the-art alternatives. Delays remain short, even for late changes, where existing methods perform worst. Moreover, the new procedure also attains higher power than current methods across broad classes of local alternatives. For mean changes, we further introduce a self-normalized version of the detector that automatically cancels out temporal dependence, eliminating the need to estimate nuisance parameters. The advantages of our approach are supported by asymptotic theory, simulations and an application to monitoring COVID19 data. Here, structural breaks associated with new virus variants are detected almost immediately by our new procedures. This indicates potential value for the real-time monitoring of future epidemics. Mathematically, our approach is underpinned by new exponential moment bounds for the global modulus of continuity of the partial sum process, which may be of independent interest beyond change point testing.