A likelihood ratio approach to sequential change point detection
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Date
2018
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Abstract
In this paper we propose a new approach for sequential monitoring of a parameter
of a d-dimensional time series. 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 longrun
variance is not necessary. We prove that for a large class of testing problems the
new detection scheme has asymptotic level a 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.
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Keywords
change point analysis, likelihood ratio principle, sequential monitoring, self-normalization