The sampling window method of Hall, Jing, and Lahiri (1998, Statistica Sinica 8, 1189–1204)
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 paper shows that the same nonparametric
subsampling method is also valid for an entirely different category of
long-range dependent series that 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.The authors thank
two referees for comments and suggestions that greatly improved an earlier
draft of the paper. This research was partially supported by U.S. National
Science Foundation grants DMS 00-72571 and DMS 03-06574 and by the
Deutsche Forschungsgemeinschaft (SFB 475).