  We consider data-adaptive wavelet estimation of a trend function in a time
series model with strongly dependent Gaussian residuals. Asymptotic expressions
for the optimal mean integrated squared error and corresponding optimal
smoothing and resolution parameters are derived. Due to adaptation to the
properties of the underlying trend function, the approach shows very good
performance for smooth trend functions while remaining competitive with minimax
wavelet estimation for functions with discontinuities. Simulations illustrate
the asymptotic results and finite-sample behavior.
