TWIN: Two window inspection for online change point detection

TL;DR

This work introduces TWIN, a two-window CUSUM framework for online change-point detection in mean and distribution, achieving logarithmic detection delays and enhanced power compared with existing methods. It provides a mean-change detector (TC) with a symmetric two-window statistic and a dual logarithmic weighting, plus a nonparametric NP-TWIN extension for distributional changes, along with extensions for dependent data via self-normalization. The authors prove a new exponential-moment modulus bound, derive limiting null distributions, and establish power-delay results under local alternatives, with practical guidance on parameter choices. Finite-sample simulations show substantially shorter delays and higher power than state-of-the-art benchmarks across subgaussian, heavy-tailed, and dependent settings, and an epidemiological case study on COVID-19 Ct values demonstrates real-time monitoring potential. The framework offers practically feasible, level-controlled monitoring with robust performance, including a self-normalized version that obviates long-run variance estimation while preserving pivotal limits.

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.

Figures (3)

• Figure 1: Detection delays displayed as box plots for normally distributed model errors and training period $N=100$. The change magnitude is $\Delta=2$ and a range of change point location $k^\star$ are considered. To be precise we have $k^\star=1$ (upper left), $k^\star=400$ (upper right), $k^\star=1000$ (lower left), $k^\star=1600$ (lower right). Numbers in brackets correspond to the median delay.
• Figure 2: Rejection rates as a function of the duration $D$ of the change. Parameters are $N=100$, $k^\star=4N$, $\Delta=2$ and errors follow a standard normal distribution.
• Figure 3: Detection times (circles) and estimated changes (crosses) for daily median Ct values. Data from DeArcosJimenez2025. The red vertical lines indicate when the strain B.1.1.519 first emerges (solid) and then becomes dominant (dashed).

Theorems & Definitions (33)

• Lemma 2.1
• Theorem 2.2
• Corollary 2.3
• Remark 2.4
• Lemma 2.5
• Theorem 2.6
• Corollary 2.7
• Theorem 2.8
• Theorem 2.9
• Corollary 2.10