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

作　　者：刘慧 万丽[1] 曾祥健 邓小成[1] LIU Hui;WAN Li;ZENG Xiang-jian;DENG Xiao-cheng(School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《广州大学学报（自然科学版）》2022年第1期41-46,共6页Journal of Guangzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目(41872246);广州大学全日制研究生基础创新资助项目(2020GDJC-M33)。

摘　　要：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.

关 键 词：降趋势波动 分形插值拟合 多重分形 HURST指数 

分 类 号：O29[理学—应用数学]