  We study how the round-off (or discretization) error changes the statistical
properties of a Gaussian long memory process. We show that the autocovariance
and the spectral density of the discretized process are asymptotically rescaled
by a factor smaller than one, and we compute exactly this scaling factor.
Consequently, we find that the discretized process is also long memory with the
same Hurst exponent as the original process. We consider the properties of two
estimators of the Hurst exponent, namely the local Whittle (LW) estimator and
the Detrended Fluctuation Analysis (DFA). By using analytical considerations
and numerical simulations we show that, in presence of round-off error, both
estimators are severely negatively biased in finite samples. Under regularity
conditions we prove that the LW estimator applied to discretized processes is
consistent and asymptotically normal. Moreover, we compute the asymptotic
properties of the DFA for a generic (i.e. non Gaussian) long memory process and
we apply the result to discretized processes.
