Abstract
A sequence of time-ordered observations possesses a trend, which is possibly subject to change at most once at some unknown time point. The aim is to test whether such an unknown change has occurred or not.
The change point methods presented here rely on ratio type test statistics based on maxima of the cumulative sums. These detection procedures for the change in regression are also robustified by considering a general score function.
The main advantage of the proposed approach is that the variance of the observations neither has to be known nor estimated. The asymptotic distribution of the test statistic under the no change null hypothesis is derived.
Moreover, we prove the consistency of the test under alternatives. The results are illustrated through a simulation study, which demonstrates computational efficiency of the procedures.
A practical application to real data is presented as well.