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Updated: Nov 15, 2025

$Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy$

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Published on: January 10, 2025

Multiscale adaptive multifractal analysis and its applications.

Guo-Sheng Han¹, Fang-Xin Zhou¹, Huan-Wen Jiang¹

¹Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, China.

Chaos (Woodbury, N.Y.)

|March 3, 2021

Summary

This summary is machine-generated.

This study introduces multiscale adaptive multifractal analysis (MAMFA) for analyzing time series data. MAMFA shows superior performance in identifying multifractal characteristics in stock market data and heart rate variability.

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Area of Science:

* Complex Systems Analysis
* Time Series Data Science
* Biomedical Signal Processing

Background:

* Accurate analysis of short-term time series requires advanced fractal analysis techniques.
* Existing multiscale multifractal analysis (MMA) has limitations in precision.
* Fractal properties are crucial for understanding complex systems like financial markets and physiological signals.

Purpose of the Study:

* To introduce a novel method, multiscale adaptive multifractal analysis (MAMFA), for precise fractal analysis.
* To evaluate MAMFA's performance against existing methods like MMA.
* To investigate the multifractal characteristics of stock market data and heart rate variability.

Main Methods:

* Development of multiscale adaptive multifractal analysis (MAMFA) by integrating adaptive fractal analysis with MMA.
* Application and comparison of MAMFA and MMA on simulated time series data.
* Analysis of Chinese and American stock indexes and R-R interval data using MAMFA.

Main Results:

* MAMFA demonstrated superior performance compared to MMA on simulated data.
* Multifractal characteristics of stock sequences are dependent on the selected scale range.
* Significant differences in Hurst surface shapes were observed between Chinese and American stock indexes, with Chinese indexes exhibiting more pronounced multifractal features.
* Abnormal heart rate subjects showed distinct Hurst surface changes compared to healthy individuals, enabling effective differentiation.

Conclusions:

* MAMFA is a more effective method for analyzing fractal properties of time series data.
* The study reveals distinct multifractal patterns in financial markets and heart rate variability.
* MAMFA can aid in distinguishing between healthy and abnormal physiological states based on heart rate variability.