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Quantifying dynamics of the financial correlations

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  • S. Drozdz
  • J. Kwapien
  • F. Gruemmer
  • F. Ruf
  • J. Speth

Abstract

A novel application of the correlation matrix formalism to study dynamics of the financial evolution is presented. This formalism allows to quantify the memory effects as well as some potential repeatable intradaily structures in the financial time-series. The present study is based on the high-frequency Deutsche Aktienindex (DAX) data over the time-period between November 1997 and December 1999 and demonstrates a power of the method. In this way two significant new aspects of the DAX evolution are identified: (i) the memory effects turn out to be sizably shorter than what the standard autocorrelation function analysis seems to indicate and (ii) there exist short term repeatable structures in fluctuations that are governed by a distinct dynamics. The former of these results may provide an argument in favour of the market efficiency while the later one may indicate origin of the difficulty in reaching a Gaussian limit, expected from the central limit theorem, in the distribution of returns on longer time-horizons.

Suggested Citation

  • S. Drozdz & J. Kwapien & F. Gruemmer & F. Ruf & J. Speth, 2001. "Quantifying dynamics of the financial correlations," Papers cond-mat/0102402, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0102402
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    Citations

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    Cited by:

    1. Stephan Süss, 2012. "The pricing of idiosyncratic risk: evidence from the implied volatility distribution," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(2), pages 247-267, June.
    2. Ormerod, Paul & Mounfield, Craig, 2002. "The convergence of European business cycles 1978–2000," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(3), pages 494-504.
    3. Diane Wilcox & Tim Gebbie, 2004. "Serial Correlation, Periodicity and Scaling of Eigenmodes in an Emerging Market," Papers cond-mat/0404416, arXiv.org, revised Sep 2007.
    4. Roehner, Bertrand M., 2005. "Stock markets are not what we think they are: the key roles of cross-ownership and corporate treasury stock," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 613-625.
    5. Kwapień, J. & Drożdż, S. & Grümmer, F. & Ruf, F. & Speth, J., 2002. "Decomposing the stock market intraday dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(1), pages 171-182.
    6. Michael C. Munnix & Rudi Schafer, 2011. "A Copula Approach on the Dynamics of Statistical Dependencies in the US Stock Market," Papers 1102.1099, arXiv.org, revised Mar 2011.
    7. Stanis{l}aw Dro.zd.z & Rafa{l} Kowalski & Pawe{l} O'swic{e}cimka & Rafa{l} Rak & Robert Gc{e}barowski, 2018. "Dynamical variety of shapes in financial multifractality," Papers 1809.06728, arXiv.org.
    8. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2021. "Financial Return Distributions: Past, Present, and COVID-19," Papers 2107.06659, arXiv.org.
    9. Münnix, Michael C. & Schäfer, Rudi, 2011. "A copula approach on the dynamics of statistical dependencies in the US stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4251-4259.
    10. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    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. Diane Wilcox & Tim Gebbie, 2004. "An analysis of Cross-correlations in South African Market data," Papers cond-mat/0402389, arXiv.org, revised Sep 2006.
    13. Marsili, Matteo & Raffaelli, Giacomo & Ponsot, Benedicte, 2009. "Dynamic instability in generic model of multi-assets markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1170-1181, May.
    14. 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.
    15. Nobi, Ashadun & Lee, Jae Woo, 2016. "State and group dynamics of world stock market by principal component analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 85-94.

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