Nonparametric estimation of a mean trend function for replicated time series is considered. The ith series is defined by Yi(j) = g(tj)+gi(tj)+Xi(j) (J=1,2,3,...) with ∑gi=0. The error processes Xi(i=1,…,k) for the individual series are assumed to be stationary with fractional differencing parameters ∈(-12,12 ) , corresponding to anti-persistence (δi < 0), short-range dependence (δi = 0) or long-range dependence (δi > 0). A non-parametric estimate of g is defined. The optimal bandwidth and optimal integrated mean squared error are derived under the assumption of fixed and randomly generated δi’s, respectively. Simulations illustrate the results.