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摘要翻译：
我们研究了单分形信号的残馀多重分形背景的存在，这种残馀多重分形背景是由于信号的有限长度和（或）由于信号所揭示的长记忆性而出现的。在人工生成的时间序列的多重分形衰减波动分析（MF-DFA）中，对这一现象进行了数值研究。接着，提供了能够描述这种信号中的多重分形内容的解析公式。最后的结果是在常用的广义Hurst指数h(q)多重分形情形下给出的，并表示为时间序列长度L和自相关指数值{\γ}的函数。本文还讨论了多重分形谱（{alpha},f（{alpha}））方法。所得结果在多重分形的任何实际应用中，包括金融数据分析中都可能具有重要意义，因为“真正的”多重分形效应应该与所谓的“多重分形噪声”清楚地分开。文中给出了金融方面的例子。文中给出的公式可以帮助我们判断是否处理真实多重分形原点的信号。
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英文标题：
《How much multifractality is included in monofractal signals?》
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作者：
Dariusz Grech, Grzegorz Pamula
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最新提交年份：
2011
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分类信息：
一级分类：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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一级分类：Physics 物理学
二级分类：Computational Physics 计算物理学
分类描述：All aspects of computational science applied to physics.
应用于物理学的计算科学的各个方面。
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一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
We investigate the presence of residual multifractal background for monofractal signals which appears due to the finite length of the signals and (or) due to the long memory the signals reveal. This phenomenon is investigated numerically within the multifractal detrended fluctuation analysis (MF-DFA) for artificially generated time series. Next, the analytical formulas enabling to describe the multifractal content in such signals are provided. Final results are shown in the frequently used generalized Hurst exponent h(q) multifractal scenario and are presented as a function of time series length L and the autocorrelation exponent value {\gamma}. The multifractal spectrum ({\alpha}, f ({\alpha})) approach is also discussed. The obtained results may be significant in any practical application of multifractality, including financial data analysis, because the "true" multifractal effect should be clearly separated from the so called "multifractal noise". Examples from finance in this context are given. The provided formulas may help to decide whether we do deal with the signal of real multifractal origin or not.
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PDF链接：
https://arxiv.org/pdf/1108.1951
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