A Sieve Bootstrap approach to constructing Prediction Intervals for Long Memory Time series

This paper is concerned with the construction of bootstrap prediction intervals for autoregressive fractionally integrated movingaverage processes which is a special class of long memory time series. For linear short-range dependent time series, the bootstrap based prediction interval is a good nonparametric alternative to those constructed under parameter assumptions. In the long memory case, we use the AR-sieve bootstrap which approximates the data generating process of a given long memory time series by a finite order autoregressive process and resamples the residuals. A simulation study is conducted to examine the performance of the AR-sieve bootstrap procedure. For the purpose of illustration a real data example is also presented.