Forecasting a Long Memory Process Subject to Structural Breaks
37 Pages Posted: 20 Aug 2013 Last revised: 26 Aug 2013
Date Written: January 19, 2013
We develop an easy-to-implement method for forecasting a stationary auto-regressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an auto-regressive (AR) model and suggest using an information criterion (AIC or Mallows’ Cp) to choose the order of the approximate AR model. Our method avoids the issue of estimation inaccuracy of the long memory parameter and the issue of spurious breaks in finite sample. Insights from our theoretical analysis are confirmed by Monte Carlo experiments, through which we also find that our method provides a substantial improvement over existing prediction methods. An empirical application to the realized volatility of three exchange rates illustrates the usefulness of our forecasting procedure. The empirical success of the HAR-RV model is explained, from an econometric perspective, by our theoretical and simulation results.
Keywords: forecasting, long memory process, structural break, HAR model
JEL Classification: C22, C53
Suggested Citation: Suggested Citation