  We study a likelihood ratio test for detecting multiple {\it 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 and changes
magnitudes. Strategies for weak change-points detection and their locations
estimates are described. The estimates are obtained as the time indices
maximizing an estimate of the local power. A simulation study shows the good
performance of our methods compared to some existing approaches. Our results
are also applied to three sets of real data.
