ARFIMA approximation and forecasting of the limiting aggregate structure of long-memory process

This article studies Man and Tiao's (2006) low-order autoregressive fractionally integrated moving-average (ARFIMA) approximation to Tsai and Chan's (2005b) limiting aggregate structure of the long-memory process. In matching the autocorrelations, we demonstrate that the approximation works well, especially for larger d values. In computing autocorrelations over long lags for larger d value, using the exact formula one might encounter numerical problems. The use of the ARFIMA(0, d, d1) model provides a useful alternative to compute the autocorrelations as a really close approximation. In forecasting future aggregates, we demonstrate the close performance of using the ARFIMA(0, d, d1) model and the exact aggregate structure. In practice, this provides a justification for the use of a low-order ARFIMA model in predicting future aggregates of long-memory process.