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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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  3. De Fabritiis, Gianni & Riccaboni, Massimo & Pammolli, Fabio, 2003. "On Size and Growth of Business Firms," MPRA Paper 15866, University Library of Munich, Germany.
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  6. Kaushik Matia & Dongfeng Fu & Sergey V. Buldyrev & Fabio Pammolli & Massimo Riccaboni & H. Eugene Stanley, 2005. "Statistical Properties of Business Firms Structure and Growth," Papers physics/0502081, arXiv.org.
  7. 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.
  8. 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.
  9. 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.
  10. Hasbrouck, Joel, 1991. " Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
  11. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2005. "Institutional Investors and Stock Market Volatility," NBER Working Papers 11722, National Bureau of Economic Research, Inc.
  12. 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.
  13. Fu, Dongfeng & Pammolli, Fabio & Buldyrev, Sergey V. & Riccaboni, Massimo & Matia, Kaushik & Yamasaki, Kazuko & Stanley, H. Eugene, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," MPRA Paper 15905, University Library of Munich, Germany.
  14. Mantegna, Rosario N. & Stanley, H.Eugene, 1998. "Modeling of financial data: Comparison of the truncated Lévy flight and the ARCH(1) and GARCH(1,1) processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 77-84.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. Kent Daniel & David Hirshleifer & Avanidhar Subrahmanyam, 1998. "Investor Psychology and Security Market Under- and Overreactions," Journal of Finance, American Finance Association, vol. 53(6), pages 1839-1885, December.
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  21. 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.
  22. 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.
  23. B. LeBaron, 2001. "Stochastic volatility as a simple generator of apparent financial power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 621-631.
  24. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161, arXiv.org.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
  31. Ivanov, Plamen Ch. & Podobnik, Boris & Lee, Youngki & Stanley, H.Eugene, 2001. "Truncated Lévy process with scale-invariant behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 154-160.
  32. Shleifer, Andrei, 2000. "Inefficient Markets: An Introduction to Behavioral Finance," OUP Catalogue, Oxford University Press, number 9780198292272.
  33. H. E. Stanley & V. Plerou, 2001. "Scaling and universality in economics: empirical results and theoretical interpretation," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 563-567.
  34. 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.
  35. 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.
  36. 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.
  37. 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.
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