Effects of dependence on local adaptability of the nonlinear wavelet estimators is examined by deriving the mean integrated squared error (MISE) in the estimation of a highly oscillating mean function of a time series. This is achieved by Showing that the MISE formula for independent observations, derived in Hall and Patil (1995a), is valid for linear stationary noise sequences. From this formula it is observed that wavelet-based estimators automatically adapt to the local features of the underlying function without the need to adjust the bandwidth.