How Independent Are Stocks in an Independent Set of a Market Graph

  • Petr A. KoldanovEmail author
  • Ivan Grechikhin
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 104)


The problem of testing hypothesis of independence of random variables describing stock returns for a given set of stocks is considered. Two tests of independence are compared. The first test is the classical maximum likelihood test based on the determinant of a sample covariance matrix. The second test is the pairwise test used for market graph construction. This test is based on testing of pairwise independence of random variables describing stock returns by Pearson correlation test. The main result is the following: the maximum likelihood test is more powerful for a wide class of alternatives. Some examples are given.


Stock Market Correlation Matrice Multivariate Normal Distribution Sample Covariance Matrix Pairwise Test 
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.



The authors are partly supported by National Research University Higher School of Economics, Russian Federation Government Grant N. 11.G34.31.0057 and RFFI Grant 14-01-00807.


  1. 1.
    Anderson, T.W.: An Introduction to Multivariate Statistical Analysis, 3rd edn. Wiley Interscience, New York (2003)zbMATHGoogle Scholar
  2. 2.
    Boginsky, V., Butenko, S., Pardalos, P.M.: On structural properties of the market graph. In: Nagurney, A. (ed.) Innovations in Financial and Economic Networks, pp. 29–45. Edward Elgar Publishing, Northampton (2003)Google Scholar
  3. 3.
    Boginski, V., Butenko, S., Pardalos, P.M.: Statistical analysis of financial networks. J. Comput. Stat. Data Anal. 48(2), 431–443 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Boginski, V., Butenko, S., Pardalos, P.M.: Mining market data: a network approach J. Comput. Oper. Res. 33(11), 3171–3184 (2006)CrossRefzbMATHGoogle Scholar
  5. 5.
    Emmert-Streib, F., Dehmer, M.: Identifying critical financial networks of DJIA: towards a network based index. Complexity 16, 1 24–33 (2010a)CrossRefGoogle Scholar
  6. 6.
    Emmert-Streib, F., Dehmer, M.: Influence of the time scale on the construction of financial networks. PLoS ONE 5, 9 (2010b)Google Scholar
  7. 7.
    Koldanov, A.P., Koldanov, P.A., Kalyagin, V.A., Pardalos, P.M.: Statistical procedures for the market graph construction. Comput. Stat. Data Anal. 68, 17–29 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses. Springer, New York (2005)zbMATHGoogle Scholar
  9. 9.
    Mantegna, R.N.: Hierarchical structure in financial market. Eur. Phys. J. B 11, 193–197 (1999)CrossRefGoogle Scholar
  10. 10.
    Tumminello, M., Aste, T., Matteo, T.D., Mantegna, R.N.: A tool for filtering information in complex systems. Proc. Natl. Acad. Sci. 102(30), 10421–10426 (2005)CrossRefGoogle Scholar
  11. 11.
    Tumminello, M., Lillo, F., Mantegna, R.N.: Correlation, hierarchies and networks in financial markets. J. Econ. Behav. Organ. 75, 40–58 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsNizhny NovgorodRussia

Personalised recommendations