Optimal prediction with nonstationary ARFIMA model

We propose two methods to predict nonstationary long-memory time series. In the first one we estimate the long-range dependent parameter d by using tapered data; we then take the nonstationary fractional filter to obtain stationary and short-memory time series. In the second method, we take successive differences to obtain a stationary but possibly long-memory time series. For the two methods the forecasts are based on those obtained from the stationary components.