For typical sample sizes occurring in economic and financial applications, the squared bias of estimators for the memory parameter is small relative to the variance. Smoothing is therefore a suitable way to improve the performance in terms of the mean squared error. However, in an analysis of financial high-frequency data, where the estimates are obtained separately for each day and then combined by averaging, the variance decreases with the sample size but the bias remains fixed. This paper proposes a method of smoothing that does not entail an increase in the bias. This method is based on the simultaneous examination of different partitions of the data. An extensive simulation study is carried out to compare it with conventional estimation methods. In this study, the new method outperforms its unsmoothed competitors with respect to the variance and its smoothed competitors with respect to the bias. Using the results of the simulation study for the proper interpretation of the empirical results obtained from a financial high-frequency dataset, we conclude that significant long-range dependencies are present only in the intraday volatility but not in the intraday returns. Finally, the robustness of these findings against daily and weekly periodic patterns is established.

中文翻译：

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减少金融高频数据的平滑对数周期图回归的偏差

对于在经济和金融应用中出现的典型样本量，内存参数的估计量的平方偏差相对于方差较小。因此，就均方误差而言，平滑是一种改善性能的合适方法。但是，在对金融高频数据进行分析时，每天分别获得估算值，然后通过求平均值相结合，方差随样本量的增加而减小，但偏差保持固定。本文提出了一种不增加偏差的平滑方法。该方法基于同时检查数据的不同分区。进行了广泛的仿真研究，以将其与常规估计方法进行比较。在这个研究中，在方差方面，新方法的表现优于未平滑的竞争对手，而在偏差方面，新方法的表现优于平滑的竞争对手。使用模拟研究的结果正确解释从金融高频数据集获得的经验结果，我们得出结论，重要的长期相关性仅存在于日内波动率中，而不存在于日内收益率中。最后，建立了这些发现相对于每日和每周定期模式的稳健性。