Higher Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes

This paper investigates the accuracy of bootstrap-based inference in the case of long memory fractionally integrated processes. The re-sampling method is based on the semi-parametric sieve approach, whereby the dynamics in the process used to produce the bootstrap draws are captured by an autoregressive approximation. Application of the sieve method to data pre-filtered by a semi-parametric estimate of the long memory parameter is also explored. Higher-order improvements yielded by both forms of re-sampling are demonstrated using Edgeworth expansions for a broad class of linear statistics. The methods are then applied to the problem of estimating the sampling distribution of the sample mean under long memory, in an experimental setting. The pre-filtered version of the bootstrap is shown to avoid the distinct underestimation of the sampling variance of the mean which the raw sieve method demonstrates in finite samples, higher order accuracy of the latter notwithstanding.