Long memory time series and short term forecasts

Abstract

This article studies the usefulness of low order ARMA models in the prediction of long memory time series with fractionally differenced ARFIMA(0, d,0) structure, −0.5< d<0.5. We argue that if the interest is in short term prediction, a suitably adapted ARMA(2,2) model can produce competitive forecasts. Numerical evaluation shows its prediction error variance is at most 0.6% higher than that of the true model at one step ahead, and at most 2.8% higher up to 10 steps ahead. However, caution needs to be taken when using the adapted ARMA model for long term prediction of strongly persistent time series. The predictability memory content of the adapted ARMA(2,2) model is also studied and compared to that of the ARFIMA(0, d,0). For illustration, we forecast the US consumer price index and inflation rates for four countries. Adapted ARMA(2,2) is compared to ARFIMA(0, d,0) fit using an out-of-sample prediction mean square errors criterion. Empirical results suggest that the performance of ARMA(2,2) compares favorably to ARFIMA(0, d,0) for forecasts up to 100 steps ahead.