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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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Universal relation between skewness and kurtosis in complex dynamics.

Matthieu Cristelli¹, Andrea Zaccaria, Luciano Pietronero

¹Department of Physics, University of Rome Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy. matthieu.cristelli@roma1.infn.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

Researchers found a skewness-kurtosis correlation in complex systems, revealing two non-Gaussian regimes. A power law regime, specific to earthquakes and financial markets, is explained by rare, dominating events.

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Area of Science:

Complex Systems Dynamics
Statistical Physics
Quantitative Finance

Background:

Non-Gaussian distributions are prevalent in complex dynamic systems.
Understanding statistical properties like skewness and kurtosis is crucial for modeling these systems.

Purpose of the Study:

To identify and analyze the correlation between skewness and kurtosis in complex dynamic systems.
To investigate two distinct regimes of non-Gaussianity, with a focus on earthquake and financial time series.

Main Methods:

Statistical analysis of time series data from earthquakes and financial markets.
Development of a theoretical model to explain observed statistical properties.

Main Results:

Identified a significant correlation between skewness and kurtosis.
Characterized two non-Gaussian regimes: parabolic and power law (exponent 4/3).
The power law regime, observed in earthquake and financial data, is modeled and attributed to the dominance of very rare events.

Conclusions:

The study reveals a universal scaling relation between skewness and kurtosis in certain complex systems.
The power law regime highlights a specific characteristic of financial markets and earthquake dynamics, driven by extreme events.
This finding contributes to understanding stylized facts in financial price fluctuations.