The effect of round-off error on long memory processes

Details The effect of round-off error on long memory processes The effect of round-off error on long memory processes

2011-07-22

arxiv.org/abs/1107.4476v2

Economy

Quantitative Finance

Statistical Finance

46 pages, 8 figures, 4 tables

Scientific paper

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.

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