Forecasting Long Memory Series Subject to Structural Change: A Two-Stage Approach

A two-stage forecasting approach for long memory time series is introduced. In the first step we estimate the fractional exponent and, applying the fractional differencing operator, we obtain the underlying weakly dependent series. In the second step, we perform the multi-step ahead forecasts for the weakly dependent series and obtain their long memory counterparts by applying the fractional cumulation operator. The methodology applies to stationary and nonstationary cases. Simulations and an application to seven time series provide evidence that the new methodology is more robust to structural change and yields good forecasting results.