  We present two approaches for linear prediction of long-memory time series.
The first approach consists in truncating the Wiener-Kolmogorov predictor by
restricting the observations to the last $k$ terms, which are the only
available values in practice. We derive the asymptotic behaviour of the
mean-squared error as $k$ tends to $ + \infty$. By contrast, the second
approach is non-parametric. An AR($k$) model is fitted to the long-memory time
series and we study the error that arises in this misspecified model.
