标题： $whittlehurst$: 一个实现惠特尔方法估计赫斯特指数的Python包 显示英文标题

标题： $whittlehurst$: A Python package implementing Whittle's likelihood estimation of the Hurst exponent

摘要： 本文介绍了一个名为$whittlehurst$的 Python 包，它实现了惠特尔（Whittle）的似然方法来估计分数布朗运动（fBm）中的 Hurst 指数。尽管惠特尔估计器的理论基础已经非常成熟，但实际和计算方面的考量对于有效使用该方法至关重要。我们明确关注评估我们的实现性能，通过分数高斯噪声（fGn）谱密度的几种数值近似，比较它们在不同输入序列长度下的计算效率、准确性和一致性。广泛的实证评估表明，我们的实现达到了最先进的估计精度和计算速度。此外，我们在合成数据和真实世界数据上将我们的方法与其他流行的 Hurst 指数估计技术进行了基准测试，强调了在将这些估计器应用于金融和生物医学数据时出现的实际考虑因素。 显示英文摘要

摘要： This paper presents $whittlehurst$, a Python package implementing Whittle's likelihood method for estimating the Hurst exponent in fractional Brownian motion (fBm). While the theoretical foundations of Whittle's estimator are well-established, practical and computational considerations are critical for effective use. We focus explicitly on assessing our implementation's performance across several numerical approximations of the fractional Gaussian noise (fGn) spectral density, comparing their computational efficiency, accuracy, and consistency across varying input sequence lengths. Extensive empirical evaluations show that our implementation achieves state-of-the-art estimation accuracy and computational speed. Additionally, we benchmark our method against other popular Hurst exponent estimation techniques on synthetic and real-world data, emphasizing practical considerations that arise when applying these estimators to financial and biomedical data.