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In this article, we propose a new approach for sequential monitoring of a general class of parameters of a d-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a closed-end method, which is motivated by the likelihood ratio test principle and compare the new method with two alternative procedures. We also incorporate self-normalization such that estimation of the long-run variance is not necessary. We prove that for a large class of testing problems the new detection scheme has asymptotic level α and is consistent. The asymptotic theory is illustrated for the important cases of monitoring a change in the mean, variance, and correlation. By means of a simulation study it is demonstrated that the new test performs better than the currently available procedures for these problems. Finally, the methodology is illustrated by a small data example investigating index prices from the dot-com bubble. Supplementary materials for this article are available online.
Dette et al. (Fri,) studied this question.