ON THE SAMPLING WINDOW METHOD FOR LONG-RANGE DEPENDENT DATA

It is known that under conditions of long-range dependence, and for ti me series subordinated to Gaussian processes, the block bootstrap meth od produces invalid estimators of the distribution of the sample mean unless the limiting distribution is normal. In this paper we show that the sampling window method produces valid, consistent estimators for non-normal as well. as normal limits. Additionally, we introduce a met hod for ''studentizing'' the sample mean of long-range dependent data, and show that sampling window approximations of its distribution are also valid. That result suggests that the sampling window method is us eful for setting confidence intervals for a population mean in a parti cularly wide range of circumstances. This conclusion is supported by a small simulation study.