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Basics of Multivariate Analysis in Neuroimaging Data
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Multifactor analysis of multiscaling in volatility return intervals.

Fengzhong Wang1, Kazuko Yamasaki, Shlomo Havlin

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2009
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Summary
This summary is machine-generated.

This study reveals that stock volatility return intervals exhibit multiscaling properties, influenced by capitalization, risk, and return, not market activity. These findings aid in understanding temporal volatility structures for portfolio optimization.

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Area of Science:

  • Quantitative Finance
  • Financial Market Analysis
  • Statistical Mechanics

Background:

  • Stock market volatility exhibits complex temporal dynamics.
  • Understanding return intervals is crucial for financial risk management.
  • Previous studies have explored volatility clustering but not the multiscaling of return intervals.

Purpose of the Study:

  • To investigate the multiscaling nature of return intervals in stock volatility.
  • To analyze the probability density function of return intervals and its dependence on volatility thresholds.
  • To identify factors influencing the multiscaling exponent gamma and its relation to stock characteristics.

Main Methods:

  • Analysis of volatility time series for 1137 U.S. stocks (2001-2002).
  • Exploration of the probability density function of return intervals (tau) using a stretched exponential model.
  • Fitting moments of tau to a power law to determine the exponent delta.
  • Investigating the dependence of gamma and delta on capitalization, risk, number of trades, and return.

Main Results:

  • The exponent gamma of the return interval distribution depends on the volatility threshold (q), supporting multiscaling.
  • Gamma is significantly influenced by capitalization, risk, and return, but not by the number of trades.
  • The power-law exponent delta also depends on capitalization, risk, and return, showing an inverse relationship with gamma.

Conclusions:

  • Stock return intervals display multiscaling behavior, linked to portfolio selection factors rather than market activity.
  • The identified multiscaling exponents (gamma and delta) provide insights into the temporal structure of volatilities.
  • These findings offer potential applications for optimizing investment portfolios by leveraging volatility dynamics.