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Identifying States of a Financial Market


  • Michael C. Munnix
  • Takashi Shimada
  • Rudi Schafer
  • Francois Leyvraz Thomas H. Seligman
  • Thomas Guhr
  • H. E. Stanley


The understanding of complex systems has become a central issue because complex systems exist in a wide range of scientific disciplines. Time series are typical experimental results we have about complex systems. In the analysis of such time series, stationary situations have been extensively studied and correlations have been found to be a very powerful tool. Yet most natural processes are non-stationary. In particular, in times of crisis, accident or trouble, stationarity is lost. As examples we may think of financial markets, biological systems, reactors or the weather. In non-stationary situations analysis becomes very difficult and noise is a severe problem. Following a natural urge to search for order in the system, we endeavor to define states through which systems pass and in which they remain for short times. Success in this respect would allow to get a better understanding of the system and might even lead to methods for controlling the system in more efficient ways. We here concentrate on financial markets because of the easy access we have to good data and because of the strong non-stationary effects recently seen. We analyze the S&P 500 stocks in the 19-year period 1992-2010. Here, we propose such an above mentioned definition of state for a financial market and use it to identify points of drastic change in the correlation structure. These points are mapped to occurrences of financial crises. We find that a wide variety of characteristic correlation structure patterns exist in the observation time window, and that these characteristic correlation structure patterns can be classified into several typical "market states". Using this classification we recognize transitions between different market states. A similarity measure we develop thus affords means of understanding changes in states and of recognizing developments not previously seen.

Suggested Citation

  • Michael C. Munnix & Takashi Shimada & Rudi Schafer & Francois Leyvraz Thomas H. Seligman & Thomas Guhr & H. E. Stanley, 2012. "Identifying States of a Financial Market," Papers 1202.1623,
  • Handle: RePEc:arx:papers:1202.1623

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    Cited by:

    1. Matthias Raddant & Friedrich Wagner, 2017. "Transitions in the stock markets of the US, UK and Germany," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 289-297, February.
    2. Desislava Chetalova & Marcel Wollschlager & Rudi Schafer, 2015. "Dependence structure of market states," Papers 1503.09004,, revised Jul 2015.
    3. Oh, Gabjin & Kim, Ho-yong & Ahn, Seok-Won & Kwak, Wooseop, 2015. "Analyzing the financial crisis using the entropy density function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 464-469.
    4. T. T. Chen & B. Zheng & Y. Li & X. F. Jiang, 2017. "New approaches in agent-based modeling of complex financial systems," Papers 1703.06840,
    5. Giacomo Livan & Jun-ichi Inoue & Enrico Scalas, 2012. "On the non-stationarity of financial time series: impact on optimal portfolio selection," Papers 1205.0877,, revised Jul 2012.
    6. Thilo A. Schmitt & Rudi Schafer & Thomas Guhr, 2016. "Credit risk: Taking fluctuating asset correlations into account," Papers 1601.03015,
    7. Li, Da-Ye & Nishimura, Yusaku & Men, Ming, 2014. "Fractal markets: Liquidity and investors on different time horizons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 144-151.
    8. Andreas Muhlbacher & Thomas Guhr, 2018. "Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations," Papers 1803.00261,
    9. Jochen Papenbrock & Peter Schwendner, 2015. "Handling risk-on/risk-off dynamics with correlation regimes and correlation networks," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 29(2), pages 125-147, May.
    10. Huang, Xuan & An, Haizhong & Gao, Xiangyun & Hao, Xiaoqing & Liu, Pengpeng, 2015. "Multiresolution transmission of the correlation modes between bivariate time series based on complex network theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 493-506.
    11. Kanjamapornkul, K. & Pinčák, Richard & Bartoš, Erik, 2016. "The study of Thai stock market across the 2008 financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 117-133.
    12. Andreas Muhlbacher & Thomas Guhr, 2017. "Extreme portfolio loss correlations in credit risk," Papers 1706.09809,
    13. Juan M. Romero & Ilse B. Zubieta-Mart'inez, 2016. "Relativistic Quantum Finance," Papers 1604.01447,
    14. repec:eee:phsmap:v:495:y:2018:i:c:p:353-392 is not listed on IDEAS
    15. Djauhari, Maman Abdurachman & Gan, Siew Lee, 2015. "Optimality problem of network topology in stocks market analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 108-114.
    16. Marcel Wollschlager & Rudi Schafer, 2015. "Impact of non-stationarity on estimating and modeling empirical copulas of daily stock returns," Papers 1506.08054,
    17. Marian Gidea, 2017. "Topology data analysis of critical transitions in financial networks," Papers 1701.06081,
    18. Yao, Can-Zhong & Lin, Ji-Nan & Zheng, Xu-Zhou & Liu, Xiao-Feng, 2015. "The study of RMB exchange rate complex networks based on fluctuation mode," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 359-376.
    19. Uechi, Lisa & Akutsu, Tatsuya & Stanley, H. Eugene & Marcus, Alan J. & Kenett, Dror Y., 2015. "Sector dominance ratio analysis of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 488-509.
    20. Nicol'o Musmeci & Tomaso Aste & Tiziana Di Matteo, 2014. "Risk diversification: a study of persistence with a filtered correlation-network approach," Papers 1410.5621,
    21. Potirakis, Stelios M. & Zitis, Pavlos I. & Eftaxias, Konstantinos, 2013. "Dynamical analogy between economical crisis and earthquake dynamics within the nonextensive statistical mechanics framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2940-2954.
    22. Desislava Chetalova & Rudi Schafer & Thomas Guhr, 2014. "Zooming into market states," Papers 1406.5386,
    23. Luu, Duc Thi & Yanovski, Boyan & Lux, Thomas, 2018. "An analysis of systematic risk in worldwide econonomic sentiment indices," Economics Working Papers 2018-03, Christian-Albrechts-University of Kiel, Department of Economics.
    24. Bundzel, Marek & Kasanický, Tomáš & Pinčák, Richard, 2016. "Using string invariants for prediction searching for optimal parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 680-688.

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