In this article, we consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown parameters of interest by proving a law of large numbers for associated variation functionals. In contrast to the semimartingale setting, the optimal window size for pre-averaging depends on the unknown roughness parameter of the underlying process. We evaluate the performance of our estimators in a simulation study and use them to empirically verify Kolmogorov's 2/3-law in turbulence data contaminated by instrument noise.

翻译：在本篇文章中,我们考虑了根据噪音高频数据估算分数过程的问题。 概括地说,预知到一个分数设置的想法,我们通过证明大量相关变异功能法则,对未知的利息参数展示了一致的测算器序列。 与半边设置不同,预知的最佳窗口大小取决于基础过程未知的粗略度参数。 我们用模拟研究来评估我们的估测器的性能,并用它们经验性地验证科尔莫戈罗夫在受仪器噪音污染的动荡数据中的2/3法律。