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Generalized permutation entropy analysis based on the two-index entropic form Sq,δ
1Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, People's Republic of China.
We introduce generalized permutation entropy (PEq,δ), a new method to analyze nonlinear time series complexity. This advanced technique enhances sensitivity to subtle changes, outperforming standard permutation entropy (PE) in detecting trends.
Area of Science:
- Nonlinear dynamics
- Statistical mechanics
- Time series analysis
Background:
- Permutation entropy (PE) quantifies nonlinear time series complexity.
- Existing methods may not capture all complexity nuances.
Purpose of the Study:
- Propose a generalized permutation entropy (PEq,δ).
- Unify existing entropic forms (Sq and Sδ).
- Enhance sensitivity to complexity changes in time series.
Main Methods:
- Developed generalized permutation entropy (PEq,δ) based on Sq,δ.
- Applied PEq,δ to synthetic and stock market data.
- Analyzed the mathematical properties of PEq,δ.
Main Results:
- PEq,δ amplifies minor complexity changes compared to PE.
- PEq,δ exhibits an exponential relationship with parameter q.
- The power k(δ) is constant when δ is determined, with power-law findings.
Conclusions:
- Generalized permutation entropy (PEq,δ) offers improved complexity analysis.
- The method shows promise for detecting subtle trends in nonlinear data.
- PEq,δ provides a unified framework with potential applications in various fields.
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