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Temporal Structure of Volatility Fluctuations

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Book cover Econophysics Approaches to Large-Scale Business Data and Financial Crisis

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Abstract

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.

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Notes

  1. 1.

    To avoid the discreteness for small τ (Eichner et al. [15] suggested a power law function for this range) and large fluctuations for very large τ, we choose the range of 0. 01 ≤ CDF ≤ 0. 50 and also use a as a free parameter to perform the stretched exponential fit.

  2. 2.

    To obtain the error bars for each point in the distribution, we produced 1,000 bootstrap resamples from the empirical data set, then compute the probability density of each of these resamples, and calculate the average and standard deviation (as shown as points and error bars in Figs. 3 and 6) for each point in the distribution. For the parameter C 1 and C 2 in (8), we use a similar method to obtain the error bars.

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Acknowledgements

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.

Author information

Authors and Affiliations

  1. Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA

    Fengzhong Wang & H. Eugene Stanley

  2. Department of Environmental Sciences, Tokyo University of Information Sciences, 4-1 Onaridai, Wakaba-ku, Chiba, 265-8501, Japan

    Kazuko Yamasaki

  3. Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Shlomo Havlin

Authors
  1. Fengzhong Wang
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  2. Kazuko Yamasaki
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  3. H. Eugene Stanley
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  4. Shlomo Havlin
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Corresponding author

Correspondence to Fengzhong Wang .

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Editors and Affiliations

  1. Department of Computational, Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, 226-8502, Japan

    Misako Takayasu (Associate Professor) (Associate Professor)

  2. Research Center for Price Dynamics and Institute of Economic Research, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo, 186-8603, Japan

    Tsutomu Watanabe (Professor) (Professor)

  3. Fundamental Research Group, Sony Computer Science Laboratories, 3-14-13 Higashigotanda, Shinagawa-ku, Tokyo, 141-0022, Japan

    Hideki Takayasu (Senior Researcher) (Senior Researcher)

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Wang, F., Yamasaki, K., Stanley, H.E., Havlin, S. (2010). Temporal Structure of Volatility Fluctuations. In: Takayasu, M., Watanabe, T., Takayasu, H. (eds) Econophysics Approaches to Large-Scale Business Data and Financial Crisis. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53853-0_4

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