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Dynamics of competition between collectivity and noise in the stock market

Author

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  • Drożdż, S
  • Grümmer, F
  • Górski, A.Z
  • Ruf, F
  • Speth, J

Abstract

Detailed study of the financial empirical correlation matrix of the 30 companies which Deutsche Aktienindex (DAX) comprised during the period of the last 11 years, using the time window of 30 trading days, is presented. This allows clear identification of a nontrivial time-dependence of the resulting correlations. In addition, as a rule, the drawdowns are always accompanied by a sizable separation of one strong collective eigenstate of the correlation matrix which, at the same time, reduces the variance of the noise states. The opposite applies to drawups. In this case, the dynamics spreads more uniformly over the eigenstates which results in an increase of the total information entropy. Analogous study of the market corresponding to Daw Jones industrial average (DJIA) leads to similar conclusions. In the latter case, however, the correlations are weaker on average. One possible reason for this effect is that the market represented by DJIA is less susceptible to various external factors than the one represented by DAX.

Suggested Citation

  • Drożdż, S & Grümmer, F & Górski, A.Z & Ruf, F & Speth, J, 2000. "Dynamics of competition between collectivity and noise in the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 440-449.
  • Handle: RePEc:eee:phsmap:v:287:y:2000:i:3:p:440-449
    DOI: 10.1016/S0378-4371(00)00383-6
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    Citations

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    Cited by:

    1. S. Drozdz & F. Gruemmer & F. Ruf & J. Speth, 2001. "Dynamics of correlations in the stock market," Papers cond-mat/0103606, arXiv.org.
    2. Eterovic, Nicolas A. & Eterovic, Dalibor S., 2013. "Separating the wheat from the chaff: Understanding portfolio returns in an emerging market," Emerging Markets Review, Elsevier, vol. 16(C), pages 145-169.
    3. Martins, André C.R., 2007. "Non-stationary correlation matrices and noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 552-558.
    4. Li, Ming-Xia & Jiang, Zhi-Qiang & Xie, Wen-Jie & Xiong, Xiong & Zhang, Wei & Zhou, Wei-Xing, 2015. "Unveiling correlations between financial variables and topological metrics of trading networks: Evidence from a stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 575-584.
    5. repec:eee:phsmap:v:495:y:2018:i:c:p:463-474 is not listed on IDEAS
    6. Conlon, T. & Ruskin, H.J. & Crane, M., 2009. "Cross-correlation dynamics in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 705-714.
    7. Pierre Cizeau & Marc Potters & Jean-Philippe Bouchaud, 2000. "Correlation structure of extreme stock returns," Science & Finance (CFM) working paper archive 0006034, Science & Finance, Capital Fund Management.
    8. Rosenow, Bernd, 2008. "Determining the optimal dimensionality of multivariate volatility models with tools from random matrix theory," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 279-302, January.
    9. Gorban, Alexander N. & Smirnova, Elena V. & Tyukina, Tatiana A., 2010. "Correlations, risk and crisis: From physiology to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3193-3217.
    10. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
    11. Wilcox, Diane & Gebbie, Tim, 2007. "An analysis of cross-correlations in an emerging market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 584-598.
    12. Wang, Gang-Jin & Xie, Chi, 2015. "Correlation structure and dynamics of international real estate securities markets: A network perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 176-193.
    13. repec:spr:qualqt:v:52:y:2018:i:3:d:10.1007_s11135-017-0502-y is not listed on IDEAS
    14. Siokis, Fotios M., 2014. "European economies in crisis: A multifractal analysis of disruptive economic events and the effects of financial assistance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 283-292.
    15. Yin, Yi & Shang, Pengjian, 2013. "Modified DFA and DCCA approach for quantifying the multiscale correlation structure of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6442-6457.
    16. Eckrot, A. & Jurczyk, J. & Morgenstern, I., 2016. "Ising model of financial markets with many assets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 250-254.
    17. Thomas Conlon & Heather J. Ruskin & Martin Crane, 2010. "Cross-Correlation Dynamics in Financial Time Series," Papers 1002.0321, arXiv.org.

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