# A new approach for open-end sequential change point monitoring

## TL;DR

This paper introduces a novel sequential change point detection method for multivariate time series that improves power and flexibility by continuously comparing estimators before and after each potential change point, outperforming existing methods.

## Contribution

The paper presents a new open-end sequential monitoring scheme that compares estimators at every time point, offering an asymptotic level $oldsymbol{ extit{ extalpha}}$ procedure with improved detection power.

## Key findings

- The new method outperforms existing procedures in simulation studies.
- It maintains an asymptotic level $ extalpha$ under no change.
- The approach is demonstrated on real data examples.

## 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 $\alpha$ 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.