  Long memory in the sense of slowly decaying autocorrelations is a stylized
fact in many time series from economics and finance. The fractionally
integrated process is the workhorse model for the analysis of these time
series. Nevertheless, there is mixed evidence in the literature concerning its
usefulness for forecasting and how forecasting based on it should be
implemented.
  Employing pseudo-out-of-sample forecasting on inflation and realized
volatility time series and simulations we show that methods based on fractional
integration clearly are superior to alternative methods not accounting for long
memory, including autoregressions and exponential smoothing. Our proposal of
choosing a fixed fractional integration parameter of $d=0.5$ a priori yields
the best results overall, capturing long memory behavior, but overcoming the
deficiencies of methods using an estimated parameter.
  Regarding the implementation of forecasting methods based on fractional
integration, we use simulations to compare local and global semiparametric and
parametric estimators of the long memory parameter from the Whittle family and
provide asymptotic theory backed up by simulations to compare different mean
estimators. Both of these analyses lead to new results, which are also of
interest outside the realm of forecasting.
