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Empirical method to measure stochasticity and multifractality in nonlinear time series
Chih-Hao Lin1, Chia-Seng Chang1, Sai-Ping Li2
1Department of Physics, National Taiwan University, Taipei 106, Taiwan and Institute of Physics, Academia Sinica, Nankang, Taipei 115, Taiwan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
Summary
This study introduces an algorithm to analyze nonlinear time series, comparing stochasticity and multifractal properties. Developed markets resemble Ito processes, while emergent markets show inefficiencies and distinct multifractal structures.
Area of Science:
- Quantitative Finance
- Complex Systems Analysis
- Statistical Modeling
Background:
- Nonlinear time series analysis is crucial for understanding complex systems.
- Stochasticity and multifractal properties characterize many real-world data series.
- Existing methods may not fully capture the dynamics of financial markets.
Purpose of the Study:
- To develop an empirical algorithm for quantifying stochasticity and multifractality in nonlinear time series.
- To compare the efficiency and market dynamics of developed versus emergent stock markets.
- To analyze differences in multifractal structures and leverage effects.
Main Methods:
- An empirical algorithm is applied to nonlinear time series.
- A parameter is defined to measure deviation from a Wiener process, assessing stochasticity.
- Local volatility is constructed to analyze multifractal structures.
Main Results:
- Developed markets exhibit dynamics close to an Ito process, indicating higher efficiency.
- Emergent markets deviate significantly from efficiency, displaying different multifractal properties.
- Distinct differences in multifractal structures and leverage effects are observed between market types.
Conclusions:
- The developed algorithm provides a quantitative method for comparing time series stochasticity and multifractality.
- Financial market efficiency varies significantly between developed and emergent economies.
- The methodology is applicable to time series analysis in various complex systems.
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