Stroe-Kunold Esther, Stadnytska Tetiana, Werner Joachim, Braun Simone
Department of Psychology, University of Heidelberg, Heidelberg, Germany.
Behav Res Methods. 2009 Aug;41(3):909-23. doi: 10.3758/BRM.41.3.909.
Recent studies have shown that many physiological and behavioral processes can be characterized by long-range correlations. The Hurst exponent H of fractal analysis and the fractional-differencing parameter d of the ARFIMA methodology are useful for capturing serial correlations. In this study, we report on different estimators of H and d implemented in R, a popular and freely available software package. By means of Monte Carlo simulations, we analyzed the performance of (1) the Geweke-Porter-Hudak estimator, (2) the approximate maximum likelihood algorithm, (3) the smoothed periodogram approach, (4) the Whittle estimator, (5) rescaled range analysis, (6) a modified periodogram, (7) Higuchi's method, and (8) detrended fluctuation analysis. The findings-confined to ARFIMA (0, d, 0) models and fractional Gaussian noise-identify the best estimators for persistent and antipersistent series. Two examples combining these results with the step-by-step procedure proposed by Delignières et al. (2006) demonstrate how this evaluation can be used as a guideline in a typical research situation.
最近的研究表明，许多生理和行为过程都具有长程相关性特征。分形分析的赫斯特指数H和自回归分数整合移动平均（ARFIMA）方法的分数差分参数d，对于捕捉序列相关性很有用。在本研究中，我们报告了在R语言（一个流行的免费软件包）中实现的H和d的不同估计方法。通过蒙特卡罗模拟，我们分析了以下方法的性能：（1）Geweke-Porter-Hudak估计方法，（2）近似最大似然算法，（3）平滑周期图方法，（4）Whittle估计方法，（5）重标极差分析，（6）修正周期图，（7）Higuchi方法，以及（8）去趋势波动分析。研究结果（限于ARFIMA(0, d, 0)模型和分数高斯噪声）确定了持续性和反持续性序列的最佳估计方法。将这些结果与Delignières等人（2006年）提出的逐步程序相结合的两个例子，展示了这种评估如何能在典型的研究情况下用作指导方针。
