Forecasts of the seasonal fractional integrated series

We study the probability of rejecting the seasonal unit root tests developed by Hylleberg et al. when they are applied to fractionally integrated seasonal time series. We find that these tests have quite low power and that they lead to a risk of over-differencing. The forecasting performance of fractionally integrated seasonal models is also examined. This approach is compared with the traditional approaches from Box–Jenkins methodology, and the HEGY-type test procedure. Forecasting results obtained from simulated series and quarterly economic time series show that the fractional approach improves the forecasting accuracy with regard to the other approaches.