Nonparametric regression with long-range and antipersistent errors is considered. Local polynomial smoothing is investigated for the estimation of the trend function and its derivatives. It is well known that in the presence of long memory (with a fractional differencing parameter 0 < d < 1/2), nonparametric regression estimators converge at a slower rate than in the case of uncorrelated or short-range dependent errors (d=0) Here, we show that in the case of antipersistence (-1/2 < d < 0), the convergence rate of a nonparametric regression estimator is faster than for uncorrelated or short-range dependent errors. Moreover, it is shown that unified asymptotic formulas for the optimal bandwidth and the MSE hold for the whole range -1/2 < d < 1/2. Also, results on estimation at the boundary are included.