We study how the round-off  error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process (i.e. the process with round-off error) 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 log-periodogram regression and the Detrended Fluctuation Analysis (DFA). By using numerical simulations and analytical considerations we show that the estimators of the Hurst exponent of the discretized process are severely negatively biased . We compute the asymptotic properties of the DFA for a generic  long memory process and we apply the result to discretized processes.
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.
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(or discretization)
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(i.e. the process with round-off error)
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log-periodogram regression
local Whittle (LW) estimator
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numerical simulations and analytical considerations
analytical considerations and numerical simulations
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the estimators of the Hurst exponent of the discretized process
, in presence of round-off error, both estimators
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. We
in finite samples. Under regularity conditions we prove that the LW estimator applied to discretized processes is consistent and asymptotically normal. Moreover, we
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(i.e. non Gaussian)