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

Author Affiliations

  • 1Department of Statistics, Islamia College University Peshawar, PAKISTAN
  • 2Department of Statistics, University of Peshawar, Peshawar, PAKISTAN

Res. J. Recent Sci., Volume 4, Issue (7), Pages 93-99, July,2 (2015)


This paper is concerned with the construction of bootstrap prediction intervals for autoregressive fractionally integrated moving-average 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.


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