Prediction Intervals for Time Series: A Modified Sieve Bootstrap Approach

Abstract

Traditional Box–Jenkins prediction intervals perform poorly when the innovations are not Gaussian. Nonparametric bootstrap procedures overcome this handicap, but most existing methods assume that the AR and MA orders of the process are known. The sieve bootstrap approach requires no such assumption but produces liberal coverage due to the use of residuals that underestimate the actual variance of the innovations and the failure of the methods to capture variations due to sampling error of the mean. A modified approach, that corrects these deficiencies, is implemented. Monte Carlo simulations results show that the modified version achieves nominal or near nominal coverage.

Keywords:

• ARMA processes
• Coverage probabilities
• Forecast intervals
• Nonparametric methods
• Resampling

Mathematics Subject Classification:

• 62M10