The Effect of Round-off Error on Long Memory Processes

44 Pages Posted: 23 Jul 2011 Last revised: 17 Mar 2013

See all articles by Gabriele La Spada

Gabriele La Spada

Federal Reserve Banks - Federal Reserve Bank of New York

Fabrizio Lillo

Università di Bologna

Date Written: July 22, 2011


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.

Keywords: long-memory processes, round-off error, measurement error, log-periodogram regression, detrended fluctuation analysis, hermite polynomials

JEL Classification: C22

Suggested Citation

La Spada, Gabriele and Lillo, Fabrizio, The Effect of Round-off Error on Long Memory Processes (July 22, 2011). Available at SSRN: or

Gabriele La Spada (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of New York ( email )

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New York, NY 10045
United States
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Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126

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