Testing for change in mean of independent multivariate observations with time varying covariance

We consider a nonparametric cusum test for change in the mean of multivariate time series with time varying covariance. we prove that under the null,the test statistic has a kolmogorov limiting distribution. the asymptotic consistency of the test against a large class of alternatives which contains abrupt,smooth and continuous changes is established. we also perform a simulation study to analyze the size distortion and the power of the proposed test. copyright 2012 mohamed boutahar.