Multi‑Fractal Detrended Fluctuation Analysis Method for Non‑Stationary Time Series Based on EMD‑LS

LUO Yuan-xing; LI Zhi-hong; LIANG Xing; LI Chao; HU Feng-cheng

doi:10.12263/DZXB.20201332

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Multi‑Fractal Detrended Fluctuation Analysis Method for Non‑Stationary Time Series Based on EMD‑LS

PAPERS | 更新时间：2025-12-08

- Multi‑Fractal Detrended Fluctuation Analysis Method for Non‑Stationary Time Series Based on EMD‑LS
- ACTA ELECTRONICA SINICA Vol. 49, Issue 12, Pages: 2323-2329(2021)
- 作者机构：
  
  1.南昌工程学院机械与电气工程学院, 江西南昌 330099
  2.南昌工程学院江西省精密驱动与控制重点实验室, 江西南昌 330099
- 作者简介：
- 基金信息：
- DOI：10.12263/DZXB.20201332
  CLC： TN911.7
- Received：26 November 2020，
  
  Revised：2021-05-06，
  
  Published：25 December 2021
- 稿件说明：
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罗远兴,李志红,梁兴等.基于EMD‑LS的非平稳时间序列多重分形去趋势波动分析方法[J].电子学报,2021,49(12):2323-2329.

LUO Yuan-xing,LI Zhi-hong,LIANG Xing,et al.Multi‑Fractal Detrended Fluctuation Analysis Method for Non‑Stationary Time Series Based on EMD‑LS[J].ACTA ELECTRONICA SINICA,2021,49(12):2323-2329.
罗远兴,李志红,梁兴等.基于EMD‑LS的非平稳时间序列多重分形去趋势波动分析方法[J].电子学报,2021,49(12):2323-2329. DOI： 10.12263/DZXB.20201332.

LUO Yuan-xing,LI Zhi-hong,LIANG Xing,et al.Multi‑Fractal Detrended Fluctuation Analysis Method for Non‑Stationary Time Series Based on EMD‑LS[J].ACTA ELECTRONICA SINICA,2021,49(12):2323-2329. DOI： 10.12263/DZXB.20201332.

摘要

多重分形去趋势波动分析(Multi‑Fractal Detrended Fluctuation Analysis

MFDFA)处理非平稳时间序列存在趋势项难以准确移除的问题，为此本文引入经验模态分解(Empirical Mode Decomposition

EMD)并通过趋势项自动判定方法提取趋势项，再利用最小二乘(Least Squares

LS)法对趋势项再拟合(EMD‑LS)，进而提出新的多重分形分析方法（EMD‑LS‑MFDFA），并针对具有理论值的二项式多重分形序列(Binomial Multifractal Sequence

BMS)，验证了EMD‑LS‑MFDFA法的有效性和稳定性，然后进行仿真分析.研究表明：相较于MFDFA方法，EMD‑LS‑MFDFA移除趋势精度更高，计算的广义Hurst指数和质量指数的均方根误差较小，其中2阶的EMD‑LS‑MFDFA具有更高的计算精度，是1阶的1.8倍，分析不同参数的BMS序列，其多重标度曲线与理论曲线相吻合，证明了该算法具有较好的稳定性和精准的分析能力.

Abstract

Multi-fractal detrended fluctuation analysis(MFDFA) deals with the problem that non-stationary time series has trend items that are difficult to accurately remove. For this reason

this paper introduces empirical mode decomposition(EMD) and adopts trend items The automatic determination method extracts the trend item

and then uses the least squares(LS) method to refit the trend item(EMD-LS)

and then proposes a new multi-fractal analysis method(EMD-LS-MFDFA)

and the binomial multi-fractal sequence(BMS) of theoretical value verifies the validity and stability of the EMD-LS-MFDFA method

and then conducts simulation analysis. Research shows that compared with the MFDFA method

EMD-LS-MFDFA has higher precision in removing trend

and the calculated generalized Hurst index and quality index have a smaller root mean square error. The calculation accuracy of the second-order EMD-LS-MFDFA is 1.8 times higher than that of the first order. The multiple scale curve is consistent with the theoretical curve by analysis of the BMS sequence of different parameters

which proves that the algorithm has good stability and accurate analysis ability.

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references

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