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A statistical physics view of financial fluctuations: Evidence for scaling and universality

  • Stanley, H. Eugene
  • Plerou, Vasiliki
  • Gabaix, Xavier

The unique scaling behavior of financial time series have attracted the research interest of physicists. Variables such as stock returns, share volume, and number of trades have been found to display distributions that are consistent with a power-law tail. We present an overview of recent research joining practitioners of economic theory and statistical physics to try to understand better some puzzles regarding economic fluctuations. One of these puzzles is how to describe outliers, i.e. phenomena that lie outside of patterns of statistical regularity. We review recent research, which suggests that such outliers may not in fact exist and that the same laws seem to govern outliers as well as day-to-day fluctuations.

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File URL: http://www.sciencedirect.com/science/article/pii/S0378437108000903
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Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 387 (2008)
Issue (Month): 15 ()
Pages: 3967-3981

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Handle: RePEc:eee:phsmap:v:387:y:2008:i:15:p:3967-3981
Contact details of provider: Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

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  10. Shleifer, Andrei, 2000. "Inefficient Markets: An Introduction to Behavioral Finance," OUP Catalogue, Oxford University Press, number 9780198292272, March.
  11. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
  12. Carbone, Anna & Stanley, H. Eugene, 2007. "Scaling properties and entropy of long-range correlated time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(1), pages 21-24.
  13. Feenberg, D.R. & Poterba, J.M., 1992. "Income Inequality and the Incomes of Very High Income Taxpayers: Evidence from Tax Returns," Working papers 92-16, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, MIT Press, vol. 121(2), pages 461-504, May.
  15. S. V. Buldyrev & L. A. N. Amaral & S. Havlin & H. Leschhorn & P. Maass & M. A. Salinger & H. E. Stanley & M. H. R. Stanley, 1997. "Scaling behavior in economics: II. Modeling of company growth," Papers cond-mat/9702085, arXiv.org.
  16. J-P. Bouchaud, 2001. "Power laws in economics and finance: some ideas from physics," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 105-112.
  17. Bagwell, Laurie Simon, 1992. " Dutch Auction Repurchases: An Analysis of Shareholder Heterogeneity," Journal of Finance, American Finance Association, vol. 47(1), pages 71-105, March.
  18. Hasbrouck, Joel, 1991. " Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
  19. Keim, Donald B. & Madhavan, Ananth, 1997. "Transactions costs and investment style: an inter-exchange analysis of institutional equity trades," Journal of Financial Economics, Elsevier, vol. 46(3), pages 265-292, December.
  20. Podobnik, Boris & Matia, Kaushik & Chessa, Alessandro & Ivanov, Plamen Ch. & Lee, Youngki & Stanley, H.Eugene, 2001. "Time evolution of stochastic processes with correlations in the variance: stability in power-law tails of distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(1), pages 300-309.
  21. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 3(2), pages 139-140, July.
  22. Rosario N. Mantegna & H. Eugene Stanley, 1998. "Modeling of Financial Data: Comparison of the Truncated L\'evy Flight and the ARCH(1) and GARCH(1,1) processes," Papers cond-mat/9804126, arXiv.org.
  23. L. A. N. Amaral & S. V. Buldyrev & S. Havlin & H. Leschhorn & P. Maass & M. A. Salinger & H. E. Stanley & M. H. R. Stanley, 1997. "Scaling behavior in economics: I. Empirical results for company growth," Papers cond-mat/9702082, arXiv.org.
  24. Sutton, John, 2002. "The variance of firm growth rates: the ‘scaling’ puzzle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(3), pages 577-590.
  25. Okuyama, K & Takayasu, M & Takayasu, H, 1999. "Zipf's law in income distribution of companies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 125-131.
  26. Fengzhong Wang & Kazuko Yamasaki & Shlomo Havlin & H. Eugene Stanley, 2005. "Scaling and memory of intraday volatility return intervals in stock market," Papers physics/0511101, arXiv.org.
  27. Parameswaran Gopikrishnan & Martin Meyer & Luis A Nunes Amaral & H Eugene Stanley, 1998. "Inverse Cubic Law for the Probability Distribution of Stock Price Variations," Papers cond-mat/9803374, arXiv.org, revised May 1998.
  28. J. Doyne Farmer & Fabrizio Lillo, 2003. "On the origin of power law tails in price fluctuations," Papers cond-mat/0309416, arXiv.org, revised Jan 2004.
  29. Youngki Lee & Luis A. N. Amaral & David Canning & Martin Meyer & H. Eugene Stanley, 1998. "Universal features in the growth dynamics of complex organizations," Papers cond-mat/9804100, arXiv.org.
  30. Vasiliki Plerou & Parameswaran Gopikrishnan & Xavier Gabaix & H. Eugene Stanley, 2004. "On the Origin of Power-Law Fluctuations in Stock Prices," Papers cond-mat/0403067, arXiv.org.
  31. Podobnik, Boris & Ivanov, Plamen Ch. & Grosse, Ivo & Matia, Kaushik & Eugene Stanley, H., 2004. "ARCH–GARCH approaches to modeling high-frequency financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 216-220.
  32. Jeffrey Wurgler & Ekaterina Zhuravskaya, 2000. "Does Arbitrage Flatten Demand Curves for Stocks?," Yale School of Management Working Papers ysm152, Yale School of Management, revised 01 Nov 2001.
  33. F. Wang & P. Weber & K. Yamasaki & S. Havlin & H. E. Stanley, 2007. "Statistical regularities in the return intervals of volatility," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 55(2), pages 123-133, 01.
  34. Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
  35. Canning, D. & Amaral, L. A. N. & Lee, Y. & Meyer, M. & Stanley, H. E., 1998. "Scaling the volatility of GDP growth rates," Economics Letters, Elsevier, vol. 60(3), pages 335-341, September.
  36. Boris Podobnik & Plamen Ch. Ivanov & Youngki Lee & Alessandro Chessa & H. Eugene Stanley, 1999. "Systems with Correlations in the Variance: Generating Power-Law Tails in Probability Distributions," Papers cond-mat/9910433, arXiv.org, revised May 2000.
  37. Chan, Louis K C & Lakonishok, Josef, 1995. " The Behavior of Stock Prices around Institutional Trades," Journal of Finance, American Finance Association, vol. 50(4), pages 1147-74, September.
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