Linear prediction of long-range dependent time series

International audienceWe 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 terms, which are the only available data in practice. We derive the asymptotic behaviour of the mean-squared error as tends to . The second predictor is the finite linear least-squares predictor the projection of the forecast value on the last observations. It is shown that these two predictors converge to the Wiener Kolmogorov predictor at the same rate