Bootstrapping forecast intervals: An application to AR(p) models

Forecast intervals typically depend upon an assumption of normal forecast errors due to lack of information concerning the distribution of the forecast. This article applies the bootstrap to the problem of estimating forecast intervals for an AR(p) model. Box-Jenkins intervals are compared to intervals produced from a naive bootstrap and a bias-correction bootstrap. Substantial differences between the three methods are found. Bootstrapping an AR(p) model requires use of the backward residuals which typically are not i.i.d. and hence inappropriate for bootstrap resampling. A recently developed method of obtaining i.i.d. backward residuals is employed and was found to affect the bootstrap prediction intervals.