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A new approach for open‐end sequential change point monitoring
Author(s) -
Gösmann Josua,
Kley Tobias,
Dette Holger
Publication year - 2021
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12555
Subject(s) - estimator , mathematics , sample (material) , multivariate statistics , series (stratigraphy) , algorithm , sample mean and sample covariance , point (geometry) , statistics , paleontology , chemistry , chromatography , biology , geometry
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 α 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.