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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Quasi-differentiation and its applications to noisy time series data from complex systems
Siew Ann Cheong1, Zheng Tien Kang2, Peter Tsung-Wen Yen2
1Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore, Republic of Singapore. cheongsa@ntu.edu.sg.
Scientific Reports
|November 7, 2025
Summary
This study introduces quasi-differentiation, a novel model-free method to extract stable states from noisy time series data. The technique successfully identified market crashes and extracted key financial data features.
Area of Science:
- Complex systems analysis
- Time series analysis
- Financial econometrics
Background:
- Analyzing complex systems with multiple stable states and state-dependent noise is challenging.
- Identifying stable states and transitions requires constructing slowly varying order parameters from noisy data.
Purpose of the Study:
- To develop a model-free method for extracting slowly varying components from noisy time series data.
- To apply this method for identifying market crashes and characterizing financial time series dynamics.
Main Methods:
- Proposed quasi-differentiation: a method using the difference between integrated information in sliding time windows.
- Developed integrated quasi-differentiation to approximate slowly varying parts of time series.
- Applied methods to Dow Jones Industrial Average (DJIA) daily returns (2003-2023).
Main Results:
- Successfully identified the Oct 2008 Lehman Brothers and Mar 2020 COVID-19 market crashes in DJIA data.
- Extracted slowly varying mean and variance of the DJIA.
- Demonstrated potential for estimating Hurst exponent and linear cross-correlation.
Conclusions:
- Quasi-differentiation and integrated quasi-differentiation are effective model-free tools for analyzing noisy time series.
- These methods have broad applicability to various complex systems beyond financial markets.
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