Estimator of a non-Gaussian parameter in multiplicative log-normal models
Ken Kiyono1, Zbigniew R Struzik, Yoshiharu Yamamoto
1College of Engineering, Nihon University, 1 Naka-gawara, Tokusada, Tamura-machi, Koriyama City, Fukushima 963-8642, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
Summary
This study introduces a new method to estimate non-Gaussian parameters in multiplicative log-normal models. The proposed estimator accurately determines theoretical values and successfully models S&P500 index fluctuations.
Area of Science:
- Statistical Physics
- Turbulence Modeling
- Financial Mathematics
Background:
- Non-Gaussian probability density functions (PDFs) are crucial for describing complex phenomena.
- Multiplicative log-normal models offer a framework for these PDFs.
- Castaing's model approximates turbulent flow velocity differences using a single non-Gaussian parameter.
Purpose of the Study:
- Propose a novel estimator for the non-Gaussian parameter in multiplicative log-normal models.
- Validate the estimator's reliability using stochastic processes.
- Investigate the scale dependence of the non-Gaussian parameter.
Main Methods:
- Developed an estimator based on the q-th order absolute moments.
- Utilized independent and identically distributed random variables.
- Employed a log-normal cascade-type multiplicative process for testing.
- Analyzed numerically generated time series.
Main Results:
- The proposed estimator reliably determines the theoretical non-Gaussian parameter.
- Scale dependence of the parameter was analyzed both analytically and numerically.
- The multiplicative log-normal model accurately describes non-Gaussian PDFs in S&P500 index fluctuations.
Conclusions:
- The new estimator provides a robust tool for analyzing multiplicative log-normal models.
- The findings have implications for understanding complex systems, including financial markets.
- The multiplicative log-normal model is a viable approach for modeling real-world non-Gaussian data.
