波动分析中去趋势方法的比较
Comparison of detrending methods for fluctuation analysis
摘要：
我们研究了最近提出的几种方法，用于检测数据序列中的长程相关性，这些方法基于与成熟的去趋势波动分析（DFA）类似的思想。特别是，我们提出了一个详细的比较定期DFA和最近提出的两种方法：中心移动平均（CMA）方法和修改后的趋势波动分析（MDFA）。我们发现，CMA在趋势较弱的长数据中的表现与DFA相当，在趋势较弱的短数据中的表现略优于DFA。当比较标准DFA与MDFA时，我们观察到DFA在我们研究的几乎所有示例中的表现都略好。我们还讨论了几种类型的趋势如何影响不同类型的DFA。对于数据中的弱趋势，新方法在这些方面与DFA相当。然而，如果数据趋势的函数形式不是先验已知的，DFA仍然是选择的方法。只有比较DFA的结果，使用不同的去趋势多项式，产生充分的认识的趋势。建议与独立方法进行比较，以证明长程相关性。
英文摘要：
We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison between the regular DFA and two recently suggested methods: the Centered Moving Average (CMA) Method and a Modified Detrended Fluctuation Analysis (MDFA). We find that CMA is performing equivalently as DFA in long data with weak trends and slightly superior to DFA in short data with weak trends. When comparing standard DFA to MDFA we observe that DFA performs slightly better in almost all examples we studied. We also discuss how several types of trends affect the different types of DFA. For weak trends in the data, the new methods are comparable with DFA in these respects. However, if the functional form of the trend in data is not a-priori known, DFA remains the method of choice. Only a comparison of DFA results, using different detrending polynomials, yields full recognition of the trends. A comparison with independent methods is recommended for proving long-range correlations.
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