Properties of a Block Bootstrap under Long-range Dependence

The block bootstrap has been largely developed for weakly dependent time processes and, in this context, much research has focused on the large- sample properties of block bootstrap inference about sample means. This work validates the block bootstrap for distribution estimation with stationary, linear processes exhibiting strong dependence. For estimating the sample mean's variance under long- memory, explicit expressions are also provided for the bias and variance of moving and non- overlapping block bootstrap estimators. These di ff er critically from the weak dependence setting and optimal blocks decrease in size as the strong dependence increases. The fi ndings in distribution and variance estimation are then illustrated using simulation.