使用不同的合成长程相关时间序列比较FA、DFA和DMA的性能
Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series
摘要：
尽管显着的努力，开发估计的长期相关性（LRC），并比较其性能，没有明确的共识存在什么是最好的方法，在何种条件下。此外，合成测试表明，LRC估计的性能不同时，使用不同的生成器的LRC时间序列。在这里，我们比较了四种估计量的性能[波动分析（FA），去趋势波动分析（DFA），向后去趋势移动平均线（BDMA）和中心去趋势移动平均线（CDMA）]。我们使用三种不同的生成器[分数高斯噪声和两种生成分数布朗运动的方法]。我们发现，CDMA有最好的性能和DFA只是在某些情况下稍差，而FA表现最差。此外，CDMA和DFA比FA对缩放范围不太敏感。因此，CDMA和DFA仍然是确定时间序列Hurst指数的“首选方法”。
英文摘要：
Notwithstanding the significant efforts to develop estimators of long-range correlations (LRC) and to compare their performance, no clear consensus exists on what is the best method and under which conditions. In addition, synthetic tests suggest that the performance of LRC estimators varies when using different generators of LRC time series. Here, we compare the performances of four estimators [Fluctuation Analysis (FA), Detrended Fluctuation Analysis (DFA), Backward Detrending Moving Average (BDMA), and centred Detrending Moving Average (CDMA)]. We use three different generators [Fractional Gaussian Noises, and two ways of generating Fractional Brownian Motions]. We find that CDMA has the best performance and DFA is only slightly worse in some situations, while FA performs the worst. In addition, CDMA and DFA are less sensitive to the scaling range than FA. Hence, CDMA and DFA remain "The Methods of Choice" in determining the Hurst index of time series.
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