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Related Experiment Video

Updated: Dec 24, 2025

Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy
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Weighted multifractal cross-correlation analysis based on Shannon entropy.

Hui Xiong1, Pengjian Shang1

  • 1Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, PR China.

Communications in Nonlinear Science & Numerical Simulation
|April 15, 2020
PubMed
Summary

A new weighted multifractal cross-correlation analysis (W-MFSMXA) method enhances time series analysis. This robust technique reveals more significant information and outperforms the original MFSMXA for shorter series, improving multifractal investigations.

Keywords:
DelayMultifractalityScaling exponent ratioShannon entropyStatistical momentsWeight

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Area of Science:

  • Quantitative Finance
  • Statistical Physics
  • Time Series Analysis

Background:

  • Traditional multifractal cross-correlation analysis based on statistical moments (MFSMXA) has limitations in capturing complex time series dynamics.
  • Existing methods may not fully extract all relevant information, especially in shorter datasets or when analyzing cross-correlations and cross-multifractality.

Purpose of the Study:

  • To introduce a novel weighted MFSMXA method based on Shannon entropy (W-MFSMXA) for improved time series cross-correlation and cross-multifractality analysis.
  • To assess the robustness and performance of the W-MFSMXA method using both artificial and real-world stock market data.
  • To provide theoretical underpinnings, including analytic formulas for a binomial multifractal model, and compare W-MFSMXA with the original MFSMXA.

Main Methods:

  • Development and application of the weighted MFSMXA method incorporating Shannon entropy.
  • Numerical experiments using artificial time series and empirical stock returns data.
  • Generation of analytic formulas for the binomial multifractal model within the W-MFSMXA framework.
  • Finite-size effect testing and generation of a scaling exponent ratio for method comparison.

Main Results:

  • The W-MFSMXA method preserves the multifractal structure while extracting more significant information compared to the standard MFSMXA.
  • W-MFSMXA demonstrates slightly superior performance over MFSMXA for shorter time series.
  • Cross-multifractality was observed in stock returns series, but this characteristic was diminished upon shuffling, indicating the removal of long memory.
  • The scaling exponent ratio between W-MFSMXA and MFSMXA approximates a centrosymmetric hyperbola.

Conclusions:

  • The proposed W-MFSMXA method offers an enhanced approach to investigating cross-correlations and cross-multifractality in time series.
  • W-MFSMXA provides a more informative analysis, particularly for shorter series, by better retaining multifractal properties and underlying data characteristics.
  • The findings highlight the presence and fragility of cross-multifractality in financial markets, linked to long-memory effects.