AbstractWe propose two methods to predict nonstationary long‐memory time series. In the first one we estimate the long‐range dependent parameterdby 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. Copyright © 2007 John Wiley & Sons, Ltd.