基于分形插值的多重分形降趋波动分析法及其有效性检验

Validity test of the fractal interpolation based multifractal detrended fluctuation analysis method

利用分形插值拟合替代多重分形降趋波动分析法(MFDFA)中的多项式拟合,给出基于分形插值的多重分形降趋波动分析法(FI-MFDFA),并以经典的二项式多重分形序列(BMS)为例,检验该方法的有效性。结果表明,FI-MFDFA方法能有效识别序列多重分布奇异性的程度,随着BMS模型参数的减小,序列多重分形特征越明显;通过与MFDFA对比分析,得出在方法步骤、参数统计精度和样本量的敏感度3个方面,FI-MFDFA方法都优于MFDFA方法,且避免了拟合阶数的选取对多重参数计算结果的影响。为进一步分析实际数据的非线性特征提供理论依据。

By using fractal interpolation fitting instead of polynomial fitting in the MFDFA method,fractal interpolation based multifractal detrended fluctuation analysis(FI-MFDFA)method is presented,and the effectiveness of this method is tested by taking the classical Binomial Multifractal Sequence(BMS)as an example.The results show that the FI-MFDFA method can effectively identify the degree of the multi-distribution singularity of sequences,and the multifractal characteristics of sequences become more obvious with the decrease of BMS model parameters.By comparing this to MFDFA,it is concluded that the FI-MFDFA method is superior to the MFDFA method in three aspects:method steps,statistical accuracy of parameters and sensitivity of sequence size.It also avoids the influence of the selection of fitting order on the calculation results of multiple parameters.It provides a theoretical basis for further analysis of the nonlinear characteristics of actual data.