A likelihood ratio approach to sequential change point detection.

In this paper we propose a new approach for sequential monitoring of aparameter of a $d$-dimensional time series. We consider a closed-end-method,which is motivated by the likelihood ratio test principle and compare the newmethod with two alternative procedures. We also incorporate self-normalizationsuch that estimation of the long-run variance is not necessary. We prove thatfor a large class of testing problems the new detection scheme has asymptoticlevel $\alpha$ and is consistent. The asymptotic theory is illustrated for theimportant cases of monitoring a change in the mean, variance and correlation.By means of a simulation study it is demonstrated that the new test performsbetter than the currently available procedures for these problems.