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Identifying States of a Financial Market

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  • Michael C. M\"unnix
  • Takashi Shimada
  • Rudi Sch\"afer
  • Francois Leyvraz Thomas H. Seligman
  • Thomas Guhr
  • H. E. Stanley
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    Abstract

    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.

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    File URL: http://arxiv.org/pdf/1202.1623
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1202.1623.

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    Date of creation: Feb 2012
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    Handle: RePEc:arx:papers:1202.1623

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    Web page: http://arxiv.org/

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    Cited by:
    1. 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, Elsevier, vol. 407(C), pages 144-151.
    2. Giacomo Livan & Jun-ichi Inoue & Enrico Scalas, 2012. "On the non-stationarity of financial time series: impact on optimal portfolio selection," Papers 1205.0877, arXiv.org, revised Jul 2012.
    3. Desislava Chetalova & Rudi Sch\"afer & Thomas Guhr, 2014. "Zooming into market states," Papers 1406.5386, arXiv.org.
    4. 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, Elsevier, vol. 392(13), pages 2940-2954.

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