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

Listed author(s):
  • 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
DOI: 10.1016/j.physa.2008.01.093
Contact details of provider: Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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;EDP Sciences, vol. 3(2), pages 139-140, July.
  7. Daniel Feenberg & James Poterba, 1992. "Income Inequality and the Incomes of Very High Income Taxpayers: Evidence from Tax Returns," NBER Working Papers 4229, National Bureau of Economic Research, Inc.
  8. 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.
  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 1147-1174, September.
  10. 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.
  11. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
  12. De Fabritiis, Gianni & Riccaboni, Massimo & Pammolli, Fabio, 2003. "On Size and Growth of Business Firms," MPRA Paper 15866, University Library of Munich, Germany.
  13. 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.
  14. 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.
  15. 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.
  16. Jeffrey Wurgler & Ekaterina Zhuravskaya, 2002. "Does Arbitrage Flatten Demand Curves for Stocks?," The Journal of Business, University of Chicago Press, vol. 75(4), pages 583-608, October.
  17. Hasbrouck, Joel, 1991. " Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
  18. 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.
  19. 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.
  20. 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;EDP Sciences, vol. 55(2), pages 123-133, 01.
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
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  31. Shleifer, Andrei, 2000. "Inefficient Markets: An Introduction to Behavioral Finance," OUP Catalogue, Oxford University Press, number 9780198292272, December.
  32. Stanley, Michael H. R. & Buldyrev, Sergey V. & Havlin, Shlomo & Mantegna, Rosario N. & Salinger, Michael A. & Eugene Stanley, H., 1995. "Zipf plots and the size distribution of firms," Economics Letters, Elsevier, vol. 49(4), pages 453-457, October.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. 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.
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