  This paper is concerned with the problem of recovering a finite,
deterministic time series from observations that are corrupted by additive,
independent noise. A distinctive feature of this problem is that the available
data exhibit long-range dependence and, as a consequence, existing statistical
theory and methods are not readily applicable. This paper gives an analysis of
the denoising problem that extends recent work of Lalley, but begins from first
principles. Both positive and negative results are established. The positive
results show that denoising is possible under somewhat restrictive conditions
on the additive noise. The negative results show that, under more general
conditions on the noise, no procedure can recover the underlying deterministic
series.
