时间序列多重分形特征的定量分析
Quantitative features of multifractal subtleties in time series
摘要：
基于多重分形去趋势波动分析（MFDFA）和小波变换模极大值（WTMM）方法，我们研究了时间序列中多重分形性的起源。序列波动根据qGaussian分布，不相关和相关的时间，使用。对于在高斯吸引域和Levy吸引域之间的边界（q=5/3）处的不相关序列，我们发现了单分形和双分形特征之间的类相过渡。这表明，这些可能只是特定的非线性时间相关性，组织成一个真正的多重分形层次的系列。为了分析多重分形的各种功能，由于这种相关性，我们使用的模型系列产生的二项式级联以及经验系列。然后，在发达的幂律相关性的时间范围内，我们发现在所有的多重分形措施的快速收敛。除了它的实际意义外，这一事实还可能反映了一个严格的q-广义中心极限定理的另一种表现形式。
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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