Abstract
A sequence of time-ordered observations follows an autore- gressive model of order one and its parameter 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.
A change point method presented here rely on a ratio type test statistic based on the maxima of cumulative sums. The main advantage of the proposed ap- proach is that the variance of the observations neither has to be known nor estimated.
Asymptotic distribution of the test statistic under the no change null hypothesis is derived. Moreover, we prove the consistency of the test under the alternative.
The results are illustrated through a simulation study, which demonstrates computational e ciency of the procedure. A practical application to real data is presented as well.