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On entropy, financial markets and minority games

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  • Zapart, Christopher A.
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    Abstract

    The paper builds upon an earlier statistical analysis of financial time series with Shannon information entropy, published in [L. Molgedey, W. Ebeling, Local order, entropy and predictability of financial time series, European Physical Journal B—Condensed Matter and Complex Systems 15/4 (2000) 733–737]. A novel generic procedure is proposed for making multistep-ahead predictions of time series by building a statistical model of entropy. The approach is first demonstrated on the chaotic Mackey–Glass time series and later applied to Japanese Yen/US dollar intraday currency data. The paper also reinterprets Minority Games [E. Moro, The minority game: An introductory guide, Advances in Condensed Matter and Statistical Physics (2004)] within the context of physical entropy, and uses models derived from minority game theory as a tool for measuring the entropy of a model in response to time series. This entropy conditional upon a model is subsequently used in place of information-theoretic entropy in the proposed multistep prediction algorithm.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 388 (2009)
    Issue (Month): 7 ()
    Pages: 1157-1172

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    Handle: RePEc:eee:phsmap:v:388:y:2009:i:7:p:1157-1172

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Entropy; Econophysics; Minority games; High-frequency financial time series; Time series prediction; Foreign exchange currency markets;

    References

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    1. J. Doyne Farmer, 1999. "Physicists Attempt to Scale the Ivory Towers of Finance," Working Papers 99-10-073, Santa Fe Institute.
    2. Damien Challet & Matteo Marsili & Yi-Cheng Zhang, 2001. "Stylized facts of financial markets and market crashes in Minority Games," Papers cond-mat/0101326, arXiv.org.
    3. Molgedey, Lutz & Ebeling, Werner, 2000. "Intraday patterns and local predictability of high-frequency financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 420-428.
    4. David Lamper & Sam Howison & Neil Johnson, 2001. "Predictability of large future changes in a competitive evolving population," OFRC Working Papers Series 2001mf01, Oxford Financial Research Centre.
    5. Emanuel Derman, 2002. "The perception of time, risk and return during periods of speculation," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 282-296.
    6. Clements, Michael P. & Franses, Philip Hans & Swanson, Norman R., 2004. "Forecasting economic and financial time-series with non-linear models," International Journal of Forecasting, Elsevier, vol. 20(2), pages 169-183.
    7. Eom, Cheoljun & Choi, Sunghoon & Oh, Gabjin & Jung, Woo-Sung, 2008. "Hurst exponent and prediction based on weak-form efficient market hypothesis of stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(18), pages 4630-4636.
    8. Emanuel Derman, 2002. "The Perception of Time, Risk and Return During Periods of Speculation," Papers cond-mat/0201345, arXiv.org.
    9. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
    10. Darbellay, Georges A & Wuertz, Diethelm, 2000. "The entropy as a tool for analysing statistical dependences in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 429-439.
    11. Paul Jefferies & Michael Hart & Neil Johnson & P.M. Hui, 2001. "From market games to real-world markets," OFRC Working Papers Series 2001mf02, Oxford Financial Research Centre.
    12. Burgos, E. & Ceva, Horacio & Perazzo, R.P.J., 2005. "Order and disorder in the local evolutionary minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 518-538.
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    Cited by:
    1. Namaki, A. & Koohi Lai, Z. & Jafari, G.R. & Raei, R. & Tehrani, R., 2013. "Comparing emerging and mature markets during times of crises: A non-extensive statistical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3039-3044.

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