Information-theoretic approach to lead-lag effect on financial markets

  • Paweł Fiedor
Open Access
Regular Article


Recently the interest of researchers has shifted from the analysis of synchronous relationships of financial instruments to the analysis of more meaningful asynchronous relationships. Both types of analysis are concentrated mostly on Pearson’s correlation coefficient and consequently intraday lead-lag relationships (where one of the variables in a pair is time-lagged) are also associated with them. Under the Efficient-Market Hypothesis such relationships are not possible as all information is embedded in the prices, but in real markets we find such dependencies. In this paper we analyse lead-lag relationships of financial instruments and extend known methodology by using mutual information instead of Pearson’s correlation coefficient. Mutual information is not only a more general measure, sensitive to non-linear dependencies, but also can lead to a simpler procedure of statistical validation of links between financial instruments. We analyse lagged relationships using New York Stock Exchange 100 data not only on an intraday level, but also for daily stock returns, which have usually been ignored.


Statistical and Nonlinear Physics 


  1. 1.
    P.A. Samuelson, Ind. Manage. Rev. 6, 41 (1965)Google Scholar
  2. 2.
    J. Tobin, J. Money Credit Bank. 1, 15 (1969)CrossRefGoogle Scholar
  3. 3.
    A. Lo, A. MacKinlay, Rev. Finance Stud. 1, 41 (1988)CrossRefGoogle Scholar
  4. 4.
    A. Shmilovici, Y. Alon-Brimer, S. Hauser, Comput. Econom. 22, 273 (2003)zbMATHCrossRefGoogle Scholar
  5. 5.
    P. Fiedor, Frequency Effects on Predictability of Stock Returns, in Proceedings of the IEEE Computational Intelligence for Financial Engineering & Economics 2014, edited by A. Serguieva, D. Maringer, V. Palade, R.J. Almeida (IEEE, London, 2014), pp. 247–254Google Scholar
  6. 6.
    B.B. Mandelbrot, J. Business 36, 394 (1963)CrossRefGoogle Scholar
  7. 7.
    L.P. Kadanoff, Simulation 16, 261 (1971)CrossRefGoogle Scholar
  8. 8.
    R.N. Mantegna, Physica A 179, 232 (1991)ADSCrossRefGoogle Scholar
  9. 9.
    R. Mantegna, Eur. Phys. J. B 11, 193 (1999)ADSCrossRefGoogle Scholar
  10. 10.
    P. Cizeau, M. Potters, J. Bouchaud, Quant. Finance 1, 217 (2001)CrossRefGoogle Scholar
  11. 11.
    K. Forbes, R. Rigobon, J. Finance 57, 2223 (2002)CrossRefGoogle Scholar
  12. 12.
    B. Podobnik, H. Stanley, Phys. Rev. Lett. 100, 084102 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    T. Aste, W. Shaw, T.D. Matteo, New J. Phys. 12, 085009 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    D. Kenett, T. Preis, G. Gur-Gershgoren, E. Ben-Jacob, Europhys. Lett. 99, 38001 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    G. Bonanno, F. Lillo, R. Mantegna, Quant. Finance 1, 96 (2001)CrossRefGoogle Scholar
  16. 16.
    M. Tumminello, T.D. Matteo, T. Aste, R. Mantegna, Eur. Phys. J. B 55, 209 (2007)ADSzbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    M. Munnix, R. Schafer, T. Guhr, Physica A 389, 4828 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    M. Billio, M. Getmansky, A. Lo, L. Pelizzon, J. Finance Econ. 104, 535 (2012)CrossRefGoogle Scholar
  19. 19.
    D. Kenett, M. Tumminello, A. Madi, G. Gur-Gershgoren, R. Mantegna, E. Ben-Jacob, PLoS ONE 5, e15032 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    P. Fiedor, Phys. Rev. E 89, 052801 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    L. Laloux, P. Cizeau, M. Potters, J. Bouchaud, Int. J. Theoret. Appl. Finance 3, 391 (2000)zbMATHCrossRefGoogle Scholar
  22. 22.
    D. Fenn, M. Porter, S. Williams, M. McDonald, N. Johnson, N. Jones, Phys. Rev. E 84, 026109 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    G. Bonanno, G. Caldarelli, F. Lillo, R. Mantegna, Phys. Rev. E 68, 046130 (2003)ADSCrossRefGoogle Scholar
  24. 24.
    J. Onnela, A. Chakraborti, K. Kaski, J. Kertesz, Physica A 324, 247 (2003)ADSzbMATHMathSciNetCrossRefGoogle Scholar
  25. 25.
    M. Tumminello, T. Aste, T.D. Matteo, R.N. Mantegna, Proc. Natl. Acad. Sci. USA 102, 10421 (2005)ADSCrossRefGoogle Scholar
  26. 26.
    M. Tumminello, T. Aste, T.D. Matteo, R.N. Mantegna, Eur. Phys. J. B 55, 209 (2007)ADSzbMATHMathSciNetCrossRefGoogle Scholar
  27. 27.
    M. Tumminello, C. Coronnello, F. Lillo, S. Micciche, R. Mantegna, Int. J. Bifurcat. Chaos 17, 2319 (2007)zbMATHCrossRefGoogle Scholar
  28. 28.
    N. Huth, F. Abergel, arXiv:1111.7103 (2011)Google Scholar
  29. 29.
    C. Curme, M. Tumminello, R. Mantegna, H. Stanley, D. Kenett, arXiv:1401.0462 (2014)Google Scholar
  30. 30.
    W.A. Brock, D.A. Hsieh, B. LeBaron, Nonlinear Dynamics, Chaos, and Instability. Statistical Theory and Economic Evidence (MIT Press, Cambridge, 1991)Google Scholar
  31. 31.
    M. Qi, J. Bus. Econ. Stat. 17, 419 (1999)Google Scholar
  32. 32.
    D. McMillan, Int. Rev. Econ. Finance 10, 353 (2001)CrossRefGoogle Scholar
  33. 33.
    D. Sornette, J. Andersen, Int. J. Mod. Phys. C 13, 171 (2002)ADSzbMATHCrossRefGoogle Scholar
  34. 34.
    K. Oh, K. Kim, Expert Syst. Appl. 22, 249 (2002)CrossRefGoogle Scholar
  35. 35.
    P.H. Franses, D.V. Dijk, J. Forecasting 15, 229 (1996)CrossRefGoogle Scholar
  36. 36.
    A. Abhyankar, L. Copeland, W. Wong, Econ. J. 105, 864 (1995)CrossRefGoogle Scholar
  37. 37.
    P. Chen, Stud. Nonlinear Dyn. Econom. 1 (1996)Google Scholar
  38. 38.
    A. Abhyankar, L. Copeland, W. Wong, J. Bus. Econ. Stat. 15, 1 (1997)Google Scholar
  39. 39.
    P.A. Ammermann, D.M. Patterson, Pacific-Basin Finance Journal 11, 175 (2003)CrossRefGoogle Scholar
  40. 40.
    D. Hsieh, J. Business 62, 339 (1989)CrossRefGoogle Scholar
  41. 41.
    R. Meese, A. Rose, Rev. Econ. Stud. 58, 603 (1991)CrossRefGoogle Scholar
  42. 42.
    C. Brooks, Appl. Finance Econ. 6, 307 (1996)CrossRefGoogle Scholar
  43. 43.
    M. Qi, Y. Wu, J. Empir. Finance 10, 623 (2003)CrossRefGoogle Scholar
  44. 44.
    T. Cover, J. Thomas, Elements of Information Theory (John Wiley & Sons, 1991)Google Scholar
  45. 45.
    F. Zhou, J. He, W. Zhong, Mutual Information based Minimum Spanning Trees Model for Selecting Discriminative Genes, in Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering (2007), pp. 1051–1055Google Scholar
  46. 46.
    F. Zhou, J. He, W. Zhong, Y. Pan, Int. J. Comput. Biol. Drug Des. 2, 187 (2009)CrossRefGoogle Scholar
  47. 47.
    A.C. Muller, S. Nowozin, C.H. Lampert, in Pattern Recognition (Springer, Berlin, 2012), Chap. Information Theoretic Clustering Using Minimum Spanning TreesGoogle Scholar
  48. 48.
    O. Sporns, D.R. Chialvo, M. Kaiser, C.C. Hilgetag, Trends Cogn. Sci. 8, 418 (2004)CrossRefGoogle Scholar
  49. 49.
    N. Brenner, O. Agam, W. Bialek, R. de Ruyter van Steveninck, Phys. Rev. Lett. 81, 4000 (1998)ADSCrossRefGoogle Scholar
  50. 50.
    N. Brenner, O. Agam, W. Bialek, R. de Ruyter van Steveninck, Phys. Rev. E 66, 031907 (2002)ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    J. Donges, Y. Zou, N. Marwan, J. Kurths, Eur. Phys. J. Special Topics 174, 157 (2009)ADSCrossRefGoogle Scholar
  52. 52.
    M. Palus, V. Komarek, T. Prochazka, Z. Hrncir, K. Sterbova, IEEE Eng. Med. Biol. 20, 65 (2001)CrossRefGoogle Scholar
  53. 53.
    A.M. Fraser, H.L. Swinney, Phys. Rev. A 33, 1134 (1986)ADSzbMATHMathSciNetCrossRefGoogle Scholar
  54. 54.
    U. Parlitz, in Nonlinear Modeling – Advanced Black-Box Techniques (Kluwer Academic Publishers, Boston, 1998), Chap. Nonlinear Time-Series AnalysisGoogle Scholar
  55. 55.
    H. Kantz, T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 2004)Google Scholar
  56. 56.
    S. Haykin, Communication Systems (John Wiley & Sons, New York, 2001)Google Scholar
  57. 57.
    F. Rossi, A. Lendasse, D. Francois, V. Wertz, M. Verleysen, Chemometr. Intell. Lab. 2, 215 (2006)CrossRefGoogle Scholar
  58. 58.
    B. Efron, R. Tibshirani, An introduction to the bootstrap (CRC press, 1993)Google Scholar
  59. 59.
    M. Tumminello, S. Miccichè, F. Lillo, J. Piilo, R. Mantegna, PLoS ONE 6, e17994 (2011)ADSCrossRefGoogle Scholar
  60. 60.
    Y. Benjamini, Y. Hochberg, J. R. Statist. Soc. B 57, 289 (1995)zbMATHMathSciNetGoogle Scholar
  61. 61.
    C.E. Shannon, Bell Syst. Tech. J. 27, 379 (1948)zbMATHMathSciNetCrossRefGoogle Scholar
  62. 62.
    J. Beirlant, E. Dudewicz, L. Gyorfi, E. van der Meulen, Int. J. Math. Stat. Sci. 6, 17 (1997)zbMATHMathSciNetGoogle Scholar
  63. 63.
    G. Darbellay, I. Vajda, IEEE T. Inform. Theory 45, 1315 (1999)zbMATHMathSciNetCrossRefGoogle Scholar
  64. 64.
    L. Paninski, Neural Comput. 15, 1191 (2003)zbMATHCrossRefGoogle Scholar
  65. 65.
    C. Daub, R. Steuer, J. Selbig, S. Kloska, BCM Bioinformatics 5, 118 (2004)CrossRefGoogle Scholar
  66. 66.
    W. Nemenman, W. Bialek, R. de Ruyter van Steveninck, Phys. Rev. E 69, 056111 (2004)ADSCrossRefGoogle Scholar
  67. 67.
    J. Bonachela, H. Hinrichsen, M. Munoz, J. Phys. A 41, 202001 (2008)ADSMathSciNetCrossRefGoogle Scholar
  68. 68.
    T. Schurmann, P. Grassberger, Chaos 6, 414 (1996)ADSMathSciNetCrossRefGoogle Scholar
  69. 69.
    D. François, V. Wertz, M. Verleysen, The permutation test for feature selection by mutual information, in European Symposium on Artificial Neural Networks, 2006, pp. 239–244Google Scholar
  70. 70.
    B. Goebel, Z. Dawy, J. Hagenauer, J. Mueller, An Approximation to the Distribution of Finite Sample Size Mutual Information Estimate, in Proc. IEEE Intl. Conf. Comm. (2005)Google Scholar
  71. 71.
    Z. Dawy, B. Goebel, J. Hagenauer, C. Andreoli, T. Meitinger, J. Mueller, IEEE/ACM Trans. Comput. Biol. Bioinf. 3, 47 (2006)CrossRefGoogle Scholar
  72. 72.
    R. Steuer, L. Molgedey, W. Ebeling, M. Jiménez-Montaño, Eur. Phys. J. B 19, 265 (2001)ADSCrossRefGoogle Scholar
  73. 73.
    N. Navet, S.H. Chen, in Natural Computing in Computational Finance, edited by T. Brabazon, M. O’Neill (Springer, 2008), Vol. 100Google Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Cracow University of EconomicsKrakówPoland

Personalised recommendations