Nonparametric kernel estimation of quantiles for time-dependent transformations of stationary Gaussian processes with long-memory was considered in Ghosh, Beran and Innes [Student 2 (1997) 109-117]. In this paper. we consider the problem of predicting the future distribution function for such processes. In particular, an expanded logistic transformation is used. Prediction intervals are obtained by using the asymptotic distribution of the predicted distribution function at future time points. Simulations and a data example illustrate the findings.