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 openend scenarios our approach yields an asymptotic level a procedure, which is consistent under the alternative of a change in the parameter.