Forecasting A Long Memory Process Subject to Structural Breaks
Cindy Shin-Huei Wang
Université catholique de Louvain, CORE, B-1348 Louvain-La-Neuve, Belgium
Luc Bauwens
Cheng Hsiao
Wang Yanan Institute for Studies in Economics (WISE), Xiamen University
11/3/2013 7:38:05 PM
We develop an easy-to-implement method for forecasting a stationary autoregressive 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 autoregressive (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 can be explained, from an econometric perspective, by our theoretical and simulation results.
Forecasting, Long memory process, Structural break, HAR model