摘要翻译：
我们研究舍入（或离散化）误差如何改变高斯长记忆过程的统计性质。我们证明了离散化过程的自协方差和谱密度是由一个小于1的因子渐近重新标度的，并且我们精确地计算了这个标度因子。因此，我们发现离散化过程也是长记忆的，具有与原过程相同的Hurst指数。本文讨论了Hurst指数的两种估计，即局部Whittle估计和减量涨落分析(DFA)的性质。通过分析和数值模拟，我们证明了在存在舍入误差的情况下，这两种估计在有限样本中都是严重负偏的。在正则性条件下，证明了应用于离散过程的LW估计是相合的和渐近正态的。此外，我们还计算了一般（即非高斯）长记忆过程的DFA的渐近性质，并将结果应用于离散化过程。
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英文标题：
《The effect of round-off error on long memory processes》
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作者：
Gabriele La Spada, Fabrizio Lillo
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最新提交年份：
2013
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  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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PDF链接：
https://arxiv.org/pdf/1107.4476