标题： 舍入误差对长记忆过程的影响 显示英文标题

标题： The effect of round-off error on long memory processes

摘要： 我们研究了舍入（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在渐近情况下按一个小于1的因子缩放，并且精确计算了这一缩放因子。 因此，我们发现离散化过程也是长记忆的，且具有与原始过程相同的赫斯特指数。 我们考虑了赫斯特指数的两种估计量的性质，即局部Whittle（LW）估计量和去趋势波动分析（DFA）。 通过使用解析方法和数值模拟，我们表明，在存在舍入误差的情况下，这两种估计量在有限样本中都严重负偏。 在正则性条件下，我们证明了应用于离散化过程的LW估计量是一致的且渐近正态的。 此外，我们计算了DFA在一般（即非高斯）长记忆过程下的渐近性质，并将其应用于离散化过程。 显示英文摘要

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.