Temporal Structure of Volatility Fluctuations

  • Fengzhong Wang
  • Kazuko Yamasaki
  • H. Eugene Stanley
  • Shlomo Havlin


Volatility fluctuations are of great importance for the study of financial markets, and the temporal structure is an essential feature of fluctuations. To explore the temporal structure, we employ a new approach based on the return interval, which is defined as the time interval between two successive volatility values that are above a given threshold. We find that the distribution of the return intervals follows a scaling law over a wide range of thresholds, and over a broad range of sampling intervals. Moreover, this scaling law is universal for stocks of different countries, for commodities, for interest rates, and for currencies. However, further and more detailed analysis of the return intervals shows some systematic deviations from the scaling law. We also demonstrate a significant memory effect in the return intervals time organization. We find that the distribution of return intervals is strongly related to the correlations in the volatility.


Probability Density Function Detrended Fluctuation Analysis Return Interval Financial Time Series Interoccurrence Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank A. Bunde, L. Muchnik, P. Weber, W.-S. Jung and I. Vodenska-Chitkushev for collaboration on many aspects of this research, and the NSF and Merck Foundation for financial support.


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Copyright information

© Springer 2010

Authors and Affiliations

  • Fengzhong Wang
    • 1
  • Kazuko Yamasaki
    • 2
  • H. Eugene Stanley
    • 1
  • Shlomo Havlin
    • 3
  1. 1.Center for Polymer Studies and Department of PhysicsBoston UniversityBostonUSA
  2. 2.Department of Environmental SciencesTokyo University of Information SciencesChibaJapan
  3. 3.Minerva Center and Department of PhysicsBar-Ilan UniversityRamat-GanIsrael

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