On detecting weak changes in the mean of CHARN models

We study a likelihood ratio test for detecting multiple weak changes in the mean of a class of CHARN models. The locally asymptotically normal (LAN) structure of the family of likelihoods under study is established. It results that the test is asymptotically optimal and an explicit form of its asymptotic local power is given as a function of candidates change locations. Weak changes locations estimates are obtained as the time indexes maximizing an estimate of the local power. A simulation study shows the good performance of our methods compared to some CUSUM approaches. Our results are also applied to three sets of real data.