Asymptotics for linear predictors of strongly dependent time series

This paper assesses the performance of finite-sample predictors as compared to forecasts based on the infinite past, in the context of long-memory processes. We establish the rate at which the autoregressive expansion based on a finite number of past observations for a large class of long-memory processes, including the popular fractional autoregressive moving average model, converges in mean square to the best linear predictor given the entire infinite past, as the number of observations increases to infinity