Forecasting costs incurred from unit differencing fractionally integrated processes

Abstract

This paper investigates the cost of assuming a unit difference when the series is only fractionally integrated with an integration parameter d≠ 1. Studies have pointed to the low power of unit root tests against a fractionally integrated alternative, and have noted the performance of these tests is worse than against nearly integrated stationary ARMA models, due to the extra persistence associated with fractional models. We look at the gains, in terms of forecasting performance, of fitting a correctly specified ARFIMA model against a mis-specified ARIMA model and ask the question as to whether the forecasting gain offsets the computational costs of estimating the correct ARFIMA model.