Validity of the sampling window method for long-range dependent linear processes

The sampling window method of Hall, Jing and Lahiri (1998) is known to consistently estimate the distribution of the sample mean for a class of long-range dependent processes, generated by transformations of Gaussian time series. This note shows that the same nonparametric subsampling method is also valid for an entirely different category of long-range dependent series which are linear with possibly non-Gaussian innovations. For these strongly dependent time processes, subsampling confidence intervals allow inference on the process mean without knowledge of the underlying innovation distribution or the long-memory parameter. The finite sample coverage accuracy of the subsampling method is examined through a numerical study.