Likens Aaron D, Mangalam Madhur, Wong Aaron Y, Charles Anaelle C, Mills Caitlin
Division of Biomechanics and Research Development, Department of Biomechanics, and Center for Research in Human Movement Variability, University of Nebraska at Omaha, 6160 University Dr S, Omaha, 68182, NE, USA.
Department of Educational Psychology, University of Minnesota, 56 East River Road, Minneapolis, 55415, MN, USA.
ArXiv. 2023 Jan 26:arXiv:2301.11262v1.
Detrended Fluctuation Analysis (DFA) is the most popular fractal analytical technique used to evaluate the strength of long-range correlations in empirical time series in terms of the Hurst exponent, . Specifically, DFA quantifies the linear regression slope in log-log coordinates representing the relationship between the time series' variability and the number of timescales over which this variability is computed. We compared the performance of two methods of fractal analysis-the current gold standard, DFA, and a Bayesian method that is not currently well-known in behavioral sciences: the Hurst-Kolmogorov (HK) method-in estimating the Hurst exponent of synthetic and empirical time series. Simulations demonstrate that the HK method consistently outperforms DFA in three important ways. The HK method: (i) accurately assesses long-range correlations when the measurement time series is short, (ii) shows minimal dispersion about the central tendency, and (iii) yields a point estimate that does not depend on the length of the measurement time series or its underlying Hurst exponent. Comparing the two methods using empirical time series from multiple settings further supports these findings. We conclude that applying DFA to synthetic time series and empirical time series during brief trials is unreliable and encourage the systematic application of the HK method to assess the Hurst exponent of empirical time series in behavioral sciences.
去趋势波动分析（DFA）是最常用的分形分析技术，用于根据赫斯特指数评估经验时间序列中长程相关性的强度。具体而言，DFA量化了对数-对数坐标中的线性回归斜率，该斜率表示时间序列的变异性与计算该变异性的时间尺度数量之间的关系。我们比较了两种分形分析方法的性能——当前的金标准DFA和行为科学中目前尚不为人熟知的贝叶斯方法：赫斯特-柯尔莫哥洛夫（HK）方法——在估计合成时间序列和经验时间序列的赫斯特指数方面的性能。模拟表明，HK方法在三个重要方面始终优于DFA。HK方法：（i）在测量时间序列较短时准确评估长程相关性，（ii）围绕中心趋势的离散度最小，（iii）产生的点估计不依赖于测量时间序列的长度或其潜在的赫斯特指数。使用来自多个设置的经验时间序列比较这两种方法进一步支持了这些发现。我们得出结论，在简短试验期间将DFA应用于合成时间序列和经验时间序列是不可靠的，并鼓励系统地应用HK方法来评估行为科学中经验时间序列的赫斯特指数。
