Long range dependence of a stationary random process usually refers to a situation when the sum of autocorrelation coefficients of the process diverges. The phenomenon of long range dependence has been observed to occur naturally in many disciplines, including Hydrology, Geology, Physics and Economics. In this talk, we consider a class of long range dependent processes that are subordinated to stationary Gaussian process with regularly varying autocorrelation functions (cf. Taqqu (1975)). We investigate the properties of the block bootstrap and the subsampling methods in the context of approximating the sampling distribution of the sample mean. Additionally, we introduce a method for "Studentizing" the sample mean of long range dependent data, which is useful for setting confidence intervals for a population mean in a particularly wide range of circumstances.
See "On the Moving Block Bootstrap under Long Range Dependence," Statistics and Probability Letters, Vol. 18, pp. 405-413, 1993. A preprinted version is available for viewing.