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Dynamics of quasi-stationary systems: Finance as an example

Author

Listed:
  • Philip Rinn
  • Yuriy Stepanov
  • Joachim Peinke
  • Thomas Guhr
  • Rudi Schafer

Abstract

We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical stability as well as transitions between different stable states are found. This combined method also allows to set up new criteria for merging clusters to simplify the complexity of the system. The low-dimensional approach allows to recover the high-dimensional fixed points of the system by means of an optimization procedure.

Suggested Citation

  • Philip Rinn & Yuriy Stepanov & Joachim Peinke & Thomas Guhr & Rudi Schafer, 2015. "Dynamics of quasi-stationary systems: Finance as an example," Papers 1502.07522, arXiv.org.
    • Handle: RePEc:arx:papers:1502.07522
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    Cited by:

    1. Heckens, Anton J. & Guhr, Thomas, 2022. "New collectivity measures for financial covariances and correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    2. Tobias Wand & Oliver Kamps & Hiroshi Iyetomi, 2024. "Causal Hierarchy in the Financial Market Network -- Uncovered by the Helmholtz-Hodge-Kodaira Decomposition," Papers 2408.12839, arXiv.org.
    3. K. Kanjamapornkul & R. Pinv{c}'ak, 2016. "Kolmogorov Space in Time Series Data," Papers 1606.03901, arXiv.org.
    4. Hirdesh K. Pharasi & Suchetana Sadhukhan & Parisa Majari & Anirban Chakraborti & Thomas H. Seligman, 2021. "Dynamics of the market states in the space of correlation matrices with applications to financial markets," Papers 2107.05663, arXiv.org.
    5. M. Mija'il Mart'inez-Ramos & Parisa Majari & Andres R. Cruz-Hern'andez & Hirdesh K. Pharasi & Manan Vyas, 2024. "Coarse graining correlation matrices according to macrostructures: Financial markets as a paradigm," Papers 2402.05364, arXiv.org, revised Jun 2024.
    6. Pharasi, Hirdesh K. & Seligman, Eduard & Sadhukhan, Suchetana & Majari, Parisa & Seligman, Thomas H., 2024. "Dynamics of market states and risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    7. Martin He{ss}ler & Tobias Wand & Oliver Kamps, 2023. "Efficient Multi-Change Point Analysis to decode Economic Crisis Information from the S&P500 Mean Market Correlation," Papers 2308.00087, arXiv.org.
    8. Gartzke, Sebastian & Wang, Shanshan & Guhr, Thomas & Schreckenberg, Michael, 2022. "Spatial correlation analysis of traffic flow on parallel motorways in Germany," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).

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