Obtaining Prediction Intervals for FARIMA Processes Using the Sieve Bootstrap

• Activity Number: 248
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Maduka N. Rupasinghe*+ and Purna Mukhopadhyay and V. A. Samaranayake
• Companies: Missouri University of Science and Technology and University of Kansas and Missouri university of Science and Technology
• Keywords: Forecasting ; Long Memory Processes ; Fractionally Intergrated Processes ; Model-based Bootstrap ; ARFIMA processes

Abstract

The Sieve Bootstrap method for constructing prediction intervals for invertible ARMA processes is based on re-samples of residuals obtained by fitting a finite degree autoregressive approximation to the time series. The advantage of this approach is that it does not require the knowledge of the orders p and q associated with the ARMA model. The application of this method has been, up to now, limited to ARMA processes whose autoregressive polynomials do not have fractional roots. In this paper we adopt the sieve bootstrap method to obtain prediction intervals for ARFIMA (p, d, q) processes with 0< d< 0.5. The proposed procedure is a simpler alternative to an existing method, which requires the estimation of p, d, and q . Monte-Carlo simulation studies, carried out under the assumption of normal, t, and exponential distributions for the innovations, show near nominal coverage under most si