This work is concerned with multivariate conditional heteroscedastic autoregressive nonlinear (CHARN) models with an unknown conditional mean function, conditional variance matrix function and density function of the distribution of noise. We study the kernel estimator of the latter function when the former are either parametric or nonparametric. The consistency, bias and asymptotic normality of the estimator are investigated. Confidence bound curves are given. A simulation experiment is performed to evaluate the performance of the results.

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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.