A new approach for open‐end sequential change point monitoring

Abstract

We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated from the remaining data, we suggest to divide the sample at each time point after the training sample. Estimators from the sample before and after all separation points are then continuously compared calculating a maximum of norms of their differences. For open-end scenarios our approach yields an asymptotic level procedure, which is consistent under the alternative of a change in the parameter. By means of a simulation study it is demonstrated that the new method outperforms the commonly used procedures with respect to power and the feasibility of our approach is illustrated by analyzing two data examples.

Designing a Statistical Procedure for Monitoring Global Carbon Dioxide Emissions

“…Recent work in the literature on sequential "on-line" testing has devised numerous interesting procedures, such as ones where the critical boundaries are dynamically adjusted based on past tests (e.g., Ramdas et al, 2017Ramdas et al, , 2018, likelihood-based methods (e.g., Dette and Gösmann, 2020), and methods that allow for open-ended monitoring periods (e.g., Gösmann et al, 2021), to name just a few examples. We note that, although such methods could potentially be useful in the present context, they would need to be adapted to the peculiar data structure encountered in our application, i.e.…”

Adaptive Change Point Monitoring for High-Dimensional Data

“…2.1 L 2 -norm-based monitoring statistics used for the closed-end procedure are no longer applicable; see Assumption 2.4 in Gösmann et al (2020) and related discussions.…”

Open-end nonparametric sequential change-point detection based on the retrospective CUSUM statistic

“…The starting point of our investigations is the recent seminal work of Gösmann, Kley and Dette (2021) who study open-end monitoring schemes sensitive to potential changes in a parameter θ (such as the mean) of a time series. A first natural approach to tackle this problem, often referred to as the ordinary CUSUM (cumulative sum) in the sequential change-point detection literature, consists of comparing an estimator θ 1:m of θ computed from the learning sample X 1 , .…”

“…, X k collected after the monitoring has started; see, e.g., Horváth et al (2004), Aue and Horváth (2004), Aue et al (2006) as well as the references given in the recent review by Kirch and Weber (2018). The idea of Gösmann, Kley and Dette (2021) is to define detectors that take into account all of the differences θ 1:j − θ j+1:k , j ∈ {m, . .…”

“…, k − 1} as a potential change-point. In their experiments, Gösmann, Kley and Dette (2021) found that their approach is not only more powerful than the ordinary CUSUM but also more powerful than the so-called Page CUSUM procedure which consists of defining a detector from the differences θ 1:m − θ j+1:k , j ∈ {m, . .…”