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Chaos in economics and finance

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  • Dominique Guegan

    (Centre d'Economie de la Sorbonne)

Abstract

In this article, we specify the different approaches followed by the economists and the financial economists in order to use chaos theory. We explain the main difference using this theory with other research domains like the mathematics and the physics. Finally, we present tools necessary for the economists and financial economists to explore this domain empirically

Suggested Citation

  • Dominique Guegan, 2007. "Chaos in economics and finance," Documents de travail du Centre d'Economie de la Sorbonne b07054, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jan 2009.
    • Handle: RePEc:mse:cesdoc:b07054
    DOI: 10.1016/j.arcontrol.2009.01.002
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    References listed on IDEAS

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    1. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
    2. Barnett,William A. & Kirman,Alan P. & Salmon,Mark, 1997. "Nonlinear Dynamics and Economics," Cambridge Books, Cambridge University Press, number 9780521471411, September.
    3. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    4. Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, number 9780521484619, September.
    5. Jess Benhabib & Kazuo Nishimura, 2012. "The Hopf Bifurcation and Existence and Stability of Closed Orbits in Multisector Models of Optimal Economic Growth," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 51-73, Springer.
    6. Dominique Guégan & Justin Leroux, 2007. "Forecasting chaotic systems: The role of local Lyapunov exponents," Cahiers de recherche 07-12, HEC Montréal, Institut d'économie appliquée.
    7. Dominique Guegan, 2005. "How can we Define the Concept of Long Memory? An Econometric Survey," Econometric Reviews, Taylor & Francis Journals, vol. 24(2), pages 113-149.
    8. Day, R H, 1992. "Complex Economic Dynamics: Obvious in History, Generic in Theory, Elusive in Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 9-23, Suppl. De.
    9. Dominique Guegan & Justin Leroux, 2009. "Local Lyapunov Exponents: A new way to predict chaotic systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00511996, HAL.
    10. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
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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. Lee, Jun Hyuk & Park, Il Seung & Ahn, Jooeun, 2023. "Noise-robust estimation of the maximal Lyapunov exponent based on state space reconstruction with principal components," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Mazzarisi, Piero & Lillo, Fabrizio & Marmi, Stefano, 2019. "When panic makes you blind: A chaotic route to systemic risk," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 176-199.
    5. Zheng, Jun & Hu, Hanping, 2022. "Bit cyclic shift method to reinforce digital chaotic maps and its application in pseudorandom number generator," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    6. Tapia Cortez, Carlos A. & Hitch, Michael & Sammut, Claude & Coulton, Jeff & Shishko, Robert & Saydam, Serkan, 2018. "Determining the embedding parameters governing long-term dynamics of copper prices," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 186-197.
    7. Lucía Inglada-Pérez & Pablo Coto-Millán, 2021. "A Chaos Analysis of the Dry Bulk Shipping Market," Mathematics, MDPI, vol. 9(17), pages 1-35, August.
    8. Wang, Fei & Zheng, Zhaowen, 2019. "Quasi-projective synchronization of fractional order chaotic systems under input saturation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    9. G. Rigatos & P. Siano & T. Ghosh, 2019. "A Nonlinear Optimal Control Approach to Stabilization of Business Cycles of Finance Agents," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1111-1131, March.
    10. C. A. Tapia Cortez & J. Coulton & C. Sammut & S. Saydam, 2018. "Determining the chaotic behaviour of copper prices in the long-term using annual price data," Palgrave Communications, Palgrave Macmillan, vol. 4(1), pages 1-13, December.
    11. Muhammad Ali Qureshi & Najeeb Alam Khan, 2024. "Clown face in 3D chaotic system integrated with memristor electronics, DNA encryption and fractional calculus," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(5), pages 1-16, May.

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    More about this item

    Keywords

    Chaos theory; attractor; Economy; Finance; estimation theory; forecasting;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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