摘要翻译：
基于多重分形离散波动分析(MFDFA)和小波变换模极大值(WTMM)方法，研究了时间序列多重分形的成因。采用时间不相关和相关的按qGaussian分布波动的序列。对于在高斯吸引盆地和Levy吸引盆地之间的边界(q=5/3)处的不相关级数，我们发现在单分形和双分形特征之间存在一个类似相位的转变。这表明，这些可能仅仅是特定的非线性时间相关性，将序列组织成一个真正的多重分形层次。为了分析由于这种相关性而产生的多重分形的各种特征，我们使用了由二项式级联生成的模型序列和经验序列。然后，在幂律相关充分发展的时间范围内，我们发现所有多重分形测度都快速收敛。这一事实除了具有实际意义外，还可以反映一个猜想的q-广义中心极限定理的另一种表现形式。
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英文标题：
《Quantitative features of multifractal subtleties in time series》
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作者：
Stanislaw Drozdz, Jaroslaw Kwapien, Pawel Oswiecimka, Rafal Rak
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最新提交年份：
2010
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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：Chaotic Dynamics        混沌动力学
分类描述：Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统，混沌，量子混沌，拓扑动力学，循环展开，湍流，传播
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
  Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian distribution, both uncorrelated and correlated in time, are used. For the uncorrelated series at the border (q=5/3) between the Gaussian and the Levy basins of attraction asymptotically we find a phase-like transition between monofractal and bifractal characteristics. This indicates that these may solely be the specific nonlinear temporal correlations that organize the series into a genuine multifractal hierarchy. For analyzing various features of multifractality due to such correlations, we use the model series generated from the binomial cascade as well as empirical series. Then, within the temporal ranges of well developed power-law correlations we find a fast convergence in all multifractal measures. Besides of its practical significance this fact may reflect another manifestation of a conjectured q-generalized Central Limit Theorem.
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PDF链接：
https://arxiv.org/pdf/0907.2866