  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.
