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Observations of deterministic chaos in financial time series by recurrence plots, can one control chaotic economy?

Author

Listed:
  • J.A. Hołyst

    (Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland)

  • M. Żebrowska

    (Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland)

  • K. Urbanowicz

    (Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland)

Abstract

Several economical time series such as exchange rates US$/British Pound, USA Treasure Bonds rates and Warsaw Stock Index WIG have been investigated using the method of recurrence plots. The percentage of recurrence REC and the percentage of determinism DET have been calculated for the original and for shuffled data. We have found that in some cases the values of REC and DET parameters are about 20% lower for the surrogate data which indicates the presence of unstable periodical orbits in the considered data. A similar result has been obtained for the chaotic Lorenz model contaminated by noise. Our investigations suggest that real economical dynamics is a mixture of deterministic and stochastic chaos. We show how a simple chaotic economic model can be controlled by appropriate influence of time-delayed feedback.

Suggested Citation

  • J.A. Hołyst & M. Żebrowska & K. Urbanowicz, 2001. "Observations of deterministic chaos in financial time series by recurrence plots, can one control chaotic economy?," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 531-535, April.
    • Handle: RePEc:spr:eurphb:v:20:y:2001:i:4:d:10.1007_pl00011109
    DOI: 10.1007/PL00011109
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    Citations

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    Cited by:

    1. Zouhaier Dhifaoui, 2022. "Determinism and Non-linear Behaviour of Log-return and Conditional Volatility: Empirical Analysis for 26 Stock Markets," South Asian Journal of Macroeconomics and Public Finance, , vol. 11(1), pages 69-94, June.
    2. Annalisa Fabretti, 2022. "A Dynamical Model for Financial Market: Among Common Market Strategies Who and How Moves the Price to Fluctuate, Inflate, and Burst?," Mathematics, MDPI, vol. 10(5), pages 1-17, February.
    3. Krishnadas M. & K. P. Harikrishnan & G. Ambika, 2022. "Recurrence measures and transitions in stock market dynamics," Papers 2208.03456, arXiv.org.
    4. Chen, Wei-Ching, 2008. "Dynamics and control of a financial system with time-delayed feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1198-1207.
    5. Urbanowicz, Krzysztof & Hołyst, Janusz A., 2004. "Investment strategy due to the minimization of portfolio noise level by observations of coarse-grained entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 284-288.
    6. Geraint Johnes & Alexander Kalinoglou & Ayana Manasova, 2005. "Chaos and the Dancing Stars," Journal of Entrepreneurship and Innovation in Emerging Economies, Entrepreneurship Development Institute of India, vol. 14(1), pages 1-19, March.
    7. Son, Woo-Sik & Park, Young-Jai, 2011. "Delayed feedback on the dynamical model of a financial system," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 208-217.
    8. Morales, Javier & Tercero, Víctor & Camacho-Vallejo, José-Fernando & Cordero, Alvaro E. & López Nerio, Luis E. & Almaguer, F-Javier, 2016. "Trend and fractality assessment of Mexico’s stock exchange," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 103-113.
    9. Yao, Can-Zhong & Lin, Qing-Wen, 2017. "Recurrence plots analysis of the CNY exchange markets based on phase space reconstruction," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 584-596.
    10. M., Krishnadas & Harikrishnan, K.P. & Ambika, G., 2022. "Recurrence measures and transitions in stock market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    11. Mostafa Shabani & Martin Magris & George Tzagkarakis & Juho Kanniainen & Alexandros Iosifidis, 2022. "Predicting the State of Synchronization of Financial Time Series using Cross Recurrence Plots," Papers 2210.14605, arXiv.org, revised Nov 2022.
    12. Monia Antar Limam, 2017. "Autosimilarty, Long Memory and Chaos: Evidence from the Tunisian Market," Business and Management Studies, Redfame publishing, vol. 3(2), pages 61-77, June.
    13. Teresa Aparicio & Dulce Saura, 2013. "Do Exchange Rate Series Present General Dependence? Some Results using Recurrence Quantification Analysis," Journal of Economics and Behavioral Studies, AMH International, vol. 5(10), pages 678-686.
    14. Orlando, Giuseppe & Bufalo, Michele, 2022. "Modelling bursts and chaos regularization in credit risk with a deterministic nonlinear model," Finance Research Letters, Elsevier, vol. 47(PA).

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