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Fluctuations and their correlations in econophysics

  • Y. Liu
  • L. A. N. Amaral
  • P. Cizeau
  • P. Gopikrishnan
  • M. Meyer
  • C.-K. Peng
  • H. E. Stanley
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 519)

Abstract

We address a current question in econophysics: Are fluctuations in economic indices correlated? To this end, we analyze 1-minute data on a stock index, the Standard and Poor index of the 500 largest stocks. We extend the 6-year data base studied by Mantegna and Stanley by including the 13 years 1984–1996 inclusive, with a recording frequency of 15 seconds. The total number of data points in this 13 years period exceed 4.5 million, which allows for a very detailed statistical analysis. We find that the fluctuations in the volatility are correlated, and that the correlations are well described by a power law.

Keywords

Fractional Brownian Motion Stock Index Detrended Fluctuation Analysis Stock Market Index Detailed Statistical Analysis 
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.

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References

  1. Admati, A., Pfleiderer, P. (1988): Review of Financial Studies 1, 3 Review of FinancialCrossRefGoogle Scholar
  2. Amaral, L.A.N., Buldyrev, S.V., Havlin, S., Salinger, M.A., Stanley, H.E. (1998): Phys. Rev. Lett. 80, 1385CrossRefADSGoogle Scholar
  3. Arneodo, A., Bacry, E., Graves, P.V., Mugy, J.F. (1995): Phys. Rev. Lett. 74, 3293CrossRefADSGoogle Scholar
  4. Bak, P., Chen, K., Scheinkman, J.A., Woodford, M. (1993): Richerche Economichi 47, 3; Scheinkman, J.A., Woodford, J. (1994): American Economic Review 84, 417zbMATHCrossRefGoogle Scholar
  5. Ball, P. (1998): The Self-Made Tapestry: Pattern Formation in Nature (Oxford University Press, Oxford)Google Scholar
  6. Barabási, A.-L., Buldyrev, S.V., Stanley, H.E., Suki, B. (1996): Phys. Rev. Lett. 76, 2192CrossRefADSGoogle Scholar
  7. Beran, J. (1994): Statistics for Long-Memory Processes (Chapman & Hall, NY)zbMATHGoogle Scholar
  8. Black, F., Scholes, M. (1973): J. of Political Economy 81, 637CrossRefGoogle Scholar
  9. Bollerslev, T. (1986): J. Econometrics 31, 307zbMATHCrossRefMathSciNetGoogle Scholar
  10. Bollerslev, T., Chou, R.Y., Kroner, K.F. (1992): J. Econometrics 52, 5; Schwert, G.W. (1989): The Journal of Finance 44, 1115; Gallant, A.R., Rossi, P.E., Tauchen, G. (1992): The Review of Financial Studies 5, 199; Le Baron, B. (1992): Journal of Business 65, 199; Chan, K., Chan, K.C., Karolyi, G.A. (1991): The Review of Financial Studies 4, 657CrossRefzbMATHGoogle Scholar
  11. Bouchaud, J.-P., Sornette, D. (1994): J. Phys. I (France) 4, 863; Sornette, D., Johansen, A., Bouchaud, J.-P. (1996): J. Phys. I (France) 6, 167.CrossRefGoogle Scholar
  12. Buldyrev, S.V., Amaral, L.A.N., Havlin, S., Leschhorn, H., Maass, P., Salinger, M.A., Stanley, H.E., Stanley, M.H.R. (1997): J. Phys. I France 7, 635CrossRefGoogle Scholar
  13. Buldyrev, S.V., Leschhorn, H., Maass, P., Stanley, H.E., Stanley, M.H.R., Amaral, L.A.N., Havlin, S., Salinger, M.A. (1997): “Scaling Behavior in Economics: Empirical Results and Modeling of Company Growth,” in Proceedings of the International School of Physics “Enrico Fermi,” Course CXXXIV, edited by F. Mallamace and H. E. Stanley (IOS Press, Amsterdam)Google Scholar
  14. Buldyrev, S.V., Amaral, L.A.N., Havlin, S., Leschhorn, H., Maass, P., Salinger, M.A., Stanley, H.E., Stanley, M.H.R. (1997): J. Phys. I France 7, 635CrossRefGoogle Scholar
  15. Bunde, A., Havlin, S. (1996): Fractals and Disordered Systems (2nd Edition), edited by A. Bunde and S. Havlin (Springer, Heidelberg)Google Scholar
  16. Cizeau, P., Liu, Y., Meyer, M., Peng, C.-K. Stanley, H.E. (1997): Physica A 245, 441CrossRefADSMathSciNetGoogle Scholar
  17. Cont, R. (1997): cond-mat/9705075Google Scholar
  18. Cox, J., Ross, S., Rubinstein, M. (1979): J. of Financial Economics 7, 229CrossRefzbMATHGoogle Scholar
  19. Dacorogna, M.M., Muller, U.A., Nagler, R.J., Olsen, R.B., Pictet, O.V. (1993): J. International Money and Finance 12, 413CrossRefGoogle Scholar
  20. Ding, Z., Granger, C.W.J., Engle, R.F. (1983): J. Empirical Finance 1, 83CrossRefGoogle Scholar
  21. Ekman, P.D. (1992): The Journal of Futures Markets 12, 365CrossRefGoogle Scholar
  22. Engle, R.F. (1982): Econometrica 50, 987zbMATHCrossRefMathSciNetGoogle Scholar
  23. Fama, E.-F. (1970): J. Finance 25, 383CrossRefGoogle Scholar
  24. Ghashghaie, S., Breymann, W., Peinke, J., Talkner, P., Dodge, Y. (1996): Nature 381, 767; see also Mantegna, R.N., Stanley, H.E. (1996): Nature 383, 587; (1997): Physica A 239, 255; and Arneodo A. et al. (preprint)CrossRefADSGoogle Scholar
  25. Granger, C.W.J., Ding, Z. (1996): J. Econometrics 73, 61zbMATHCrossRefMathSciNetGoogle Scholar
  26. Harris, L. (1986): J. of Financial Economics 16, 99CrossRefGoogle Scholar
  27. Hausdorff, J.M., Purdon, P.L., Peng, C.-K., Ladin, Z., Wei, J.Y., Goldberger, A.L. (1996): J Appl Physiol 80, 1448–1457Google Scholar
  28. Hausdorff, J.M., Peng, C.-K. (1996): Phys Rev E 54, 2154–2157CrossRefADSGoogle Scholar
  29. Hirabayashi, T., Takayayasu, H., Miura, H., Hamada, K. (1993): Fractals 1, 29–40zbMATHCrossRefGoogle Scholar
  30. Ivanov, P.Ch., Rosenblum, M.G., Peng, C.-K., Mietus, J., Havlin, S., Stanley, H.E., Goldberger, A.L. (1996): Nature 383, 323CrossRefADSGoogle Scholar
  31. Ivanov, P.Ch., Rosenblum, M.G., Peng, C.-K., Mietus, J., Havlin, S., Stanley, H.E., Goldberger, A.L. (1998): Physica A 249, 587–593CrossRefGoogle Scholar
  32. Iyengar, N., Peng, C.-K., Morin, R., Goldberger, A.L., Lipsitz, L.A. (1997): Am J Physiol 271, R1078–R1084Google Scholar
  33. Keitt, T., Stanley, H.E. (1998): “Dynamics of North American Breeding Bird Populations,” Nature 393, 257CrossRefADSGoogle Scholar
  34. Keitt, T., Stanley, H.E. (preprint): “Lévy Flights and 1/f Noise in High Abundance Populations”Google Scholar
  35. Knobler, C.M., Robledo, A., Stanley, H.E. (1997): Statistical Mechanics in the Physical, Biological, and Social Sciences: Festschrift in Honor of Benjamin Widom on the occasion of his 70th Birthday (Elsevier, Amsterdam, 1997) [Published as a special issue of Physica A 244 Google Scholar
  36. Kolmogorov, A.N. (1961): Local structure of turbulence in fluid for very large Reynolds numbers. In Transl in Turbulence. Friedlander SK and Topper L, eds. (Interscience Publishers, New York), pp. 151–155Google Scholar
  37. Krugman, P.R. (1996): The Self-Organizing Economy (Blackwell Publishers, Cambridge)Google Scholar
  38. Levy, M., Levy, H., Solomon, S. (1994): Economics Letters 45, 103–111; Levy, M., Levy, H., Solomon, S. (1995): J. Phys. I 5, 1087–1107zbMATHCrossRefGoogle Scholar
  39. Levy, M., Persky, N., Solomon, S. (1996): Int. J. of High Speed Computing 8, 93–113; Levy, M., and Solomon, S. (1996): Int. J. Mod. Phys. C 4, 7CrossRefGoogle Scholar
  40. Liu, Y., Cizeau, P., Meyer, M., Peng, C.-K., Stanley, H.E. (1997): Physica A 245, 437CrossRefADSMathSciNetGoogle Scholar
  41. Makse, H.A., Havlin, S., Stanley, H.E. (1995): Nature 377, 608 Makse, H.A., Andrade, J., Batty, M., Havlin, S., Stanley, H.E., preprint: “Modeling Urban Growth Patterns with Correlated Percolation”CrossRefADSGoogle Scholar
  42. Makse, H.A., Cizeau, P., Stanley, H.E. (1997): Phys. Rev. Lett. 78, 3298CrossRefADSGoogle Scholar
  43. Makse, H.A., Havlin, S., King, P.R., Stanley, H.E. (1997): Nature 386, 379CrossRefADSGoogle Scholar
  44. Makse, H.A., Cizeau, P., Havlin, S., King, P.R., Stanley, H.E. (1998): “Spontaneous Self-Stratification Without Shaking: ‘Potatoes from Mashed Potatoes'” [Proc. 1997 NATO ASI] in Granular Matter, edited by H. J. Herrmann (Kluwer, Dordrecht)Google Scholar
  45. Makse, H.A., Cizeau, P., Stanley, H.E. (1998): Physica A 249, 391; Makse, H.A., Havlin, S., King, P.R., Stanley, H.E. (1998): Proc. Minerva Conf., Phil. Mag. 77, 1341–1351CrossRefGoogle Scholar
  46. Makse, H.A., Ball, R.C., Stanley, H.E., Warr, S. (1998): “Dynamics of Granular Self-Stratification,” Phys. Rev. E 58 Google Scholar
  47. Mandelbrot, B.B. (1997): Fractals and Scaling in Finance: Discontinuity, Concentration, Risk (Springer-Verlag, New York)zbMATHGoogle Scholar
  48. Mandelbrot, B.B. (1963): J. Business 36, 393Google Scholar
  49. Mandelbrot, B.B., van Ness, J.W. (1968): SIAM Rev. 10, 422zbMATHCrossRefMathSciNetADSGoogle Scholar
  50. Mantegna, R.N., Stanley, H.E. (1995): Nature 376, 46; (1994): Phys. Rev. Lett. 73, 2946CrossRefADSGoogle Scholar
  51. Mantegna, R.N., Stanley, H.E. (1997): “Physics Investigation of Financial Markets,” in Proceedings of the International School of Physics “Enrico Fermi,” Course CXXXIV, edited by F. Mallamace and H. E. Stanley (IOS Press, Amsterdam, 1997); Econophysics (Cambridge University Press, under contract)Google Scholar
  52. Peng, C.-K., Buldyrev, S.V., Goldberger, A.L., Havlin, S., Sciortino, F., Simons, M., Stanley, H.E. (1992): Nature 356, 168CrossRefADSGoogle Scholar
  53. Peng, C.-K., Mietus, J., Hausdorff, J.M., Havlin, S., Stanley, H.E., Goldberger, A.L. (1993) Phys. Rev. Lett. 70, 1343CrossRefADSGoogle Scholar
  54. Peng, C.-K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., Goldberger, A.L. (1994): Phys. Rev. E 49, 1684CrossRefADSGoogle Scholar
  55. Peng, C.-K., Havlin, S., Stanley, H.E., Goldberger, A.L. (1995): Chaos 5, 82CrossRefADSGoogle Scholar
  56. Peterson, I. (1996): Science News 150, 104CrossRefGoogle Scholar
  57. Peterson, I. (1997): The Jungles of Randomness (New York: Viking)Google Scholar
  58. Potters, M., Cont, R., Bouchaud, J.-P. (preprint): “Financial markets as adaptative systems”Google Scholar
  59. Stanley, H.E. (1971): Introduction to Phase Transitions and Critical Phenomena (Oxford, Oxford University Press)Google Scholar
  60. Stanley, M.H.R., Amaral, L.A.N., Buldyrev, S.V., Havlin, S., Leschhorn, H., Maass, P., Salinger, M.A., Stanley, H.E. (1996): Nature 379, 804CrossRefADSGoogle Scholar
  61. Stanley, M.H.R., Amaral, L.A.N., Buldyrev, S.V., Havlin, S., Leschhorn, H., Maass, P., Salinger, M.A., Stanley, H.E. (1996): Nature 379, 804CrossRefADSGoogle Scholar
  62. Suki, B., Barabási, A.-L., Hantos, Z., Peták, F., Stanley, H.E. (1994): Nature 368, 615–618CrossRefADSGoogle Scholar
  63. Takayayasu, H., Miura, H., Hirabayashi, T., Hamada, K. (1992): Physica A 184, 127–134CrossRefADSGoogle Scholar
  64. Takayasu, H., Okuyama, K. (1998): Fractals 6, 67–79CrossRefGoogle Scholar
  65. Wood, R.A., McInish, T.H., Ord, J.K. (1985) J. of Finance 40, 723CrossRefGoogle Scholar
  66. Vespignani, A., Zapperi, S. (1997): Phys. Rev. Lett. 78, 4793CrossRefADSGoogle Scholar
  67. Viswanathan, G.M., Afanasyev, V., Buldyrev, S.V., Murphy, E.J., Prince, P.A., Stanley, H.E. (1996): Nature 381, 413CrossRefADSGoogle Scholar
  68. Viswanathan, G.M., Buldyrev, S.V., Havlin, S., da Luz, M.G., Raposo, E., Stanley, H.E. (submitted): “Optimizing Success in Random Foraging: A Physical Approach,” Phys. Rev. Lett.Google Scholar
  69. Zanette, D., Manrubia, S. (1997): Phys. Rev. Lett. 79, 323CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Y. Liu
    • 1
  • L. A. N. Amaral
    • 1
  • P. Cizeau
    • 1
  • P. Gopikrishnan
    • 1
  • M. Meyer
    • 1
  • C.-K. Peng
    • 1
  • H. E. Stanley
    • 1
  1. 1.Center for Polymer Studies and Department of PhysicsBoston UniversityBostonUSA

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