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Dynamics of competition between collectivity and noise in the stock market

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

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437100003836
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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 287 (2000)
    Issue (Month): 3 ()
    Pages: 440-449

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    Handle: RePEc:eee:phsmap:v:287:y:2000:i:3:p:440-449

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

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    Cited by:
    1. 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.
    2. Pierre Cizeau & Marc Potters & Jean-Philippe Bouchaud, 2000. "Correlation structure of extreme stock returns," Papers cond-mat/0006034, arXiv.org, revised Jan 2001.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. S. Drozdz & F. Gruemmer & F. Ruf & J. Speth, 2001. "Dynamics of correlations in the stock market," Papers cond-mat/0103606, arXiv.org.
    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. Thomas Conlon & Heather J. Ruskin & Martin Crane, 2010. "Cross-Correlation Dynamics in Financial Time Series," Papers 1002.0321, arXiv.org.

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