On the Effects of Imposing or Ignoring Long Memory when Forecasting

Since the true nature of a time series process is often unknown it is important to understand the effects of model choice. This paper examines how the choice between modelling stationary time series as ARMA or ARFIMA processes affects the accuracy of forecasts. This is done, for first-order autoregressions and moving averages and for ARFIMA 1,d,0) processes, by means of a Monte Carlo simulation study. The fractional models are estimated using the technique of Geweke and Porter-Hudak, the modified rescaled range and the maximum likelihood procedure. We conclude that ignoring long memory is worse than imposing it, when forecasting, and that the ML estimator is preferred.