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Testing chaotic dynamics via Lyapunov exponents

Author

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  • Simón Sosvilla-Rivero

    (FEDEA and Universidad Complutense de Madrid, Spain)

  • Fernando Fernández-Rodriguez

    (Department of Quantitative Methods in Economics and Management, Universidad de Las Palmas de Gran Canaria, Spain)

  • Julián Andrada-Félix

    (Department of Quantitative Methods in Economics and Management, Universidad de Las Palmas de Gran Canaria, Spain)

Abstract

We propose a new test to detect chaotic dynamics, based on the stability of the largest Lyapunov exponent from different sample sizes. This test is applied to the data used in the single-blind controlled competition tests for non-linearity and chaos that were generated by Barnett et al. (1997), as well as to several other chaotic series. The results suggest that the new test is particularly effective when compared to other stochastic alternatives (both linear and non-linear). For large sample sizes the power of the test is one, although for small sample sizes it diminishes occasionally. Copyright © 2005 John Wiley & Sons, Ltd.

Suggested Citation

  • Simón Sosvilla-Rivero & Fernando Fernández-Rodriguez & Julián Andrada-Félix, 2005. "Testing chaotic dynamics via Lyapunov exponents," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 911-930.
    • Handle: RePEc:jae:japmet:v:20:y:2005:i:7:p:911-930
    DOI: 10.1002/jae.805
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    Cited by:

    1. Loretta Mastroeni & Pierluigi Vellucci, 2016. "“Butterfly Effect" vs Chaos in Energy Futures Markets," Departmental Working Papers of Economics - University 'Roma Tre' 0209, Department of Economics - University Roma Tre.
    2. Hartwell, Christopher A., 2019. "Short waves in Hungary, 1923 and 1946: Persistence, chaos, and (lack of) control," Journal of Economic Behavior & Organization, Elsevier, vol. 163(C), pages 532-550.
    3. Park, Joon Y. & Whang, Yoon-Jae, 2012. "Random walk or chaos: A formal test on the Lyapunov exponent," Journal of Econometrics, Elsevier, vol. 169(1), pages 61-74.
    4. Matilla-García, Mariano & Marín, Manuel Ruiz, 2010. "A new test for chaos and determinism based on symbolic dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 600-614, December.
    5. Bask, Mikael & Widerberg, Anna, 2009. "Market structure and the stability and volatility of electricity prices," Energy Economics, Elsevier, vol. 31(2), pages 278-288, March.
    6. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    7. Belaire-Franch, Jorge, 2018. "Exchange rates expectations and chaotic dynamics: A replication study," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-9.
    8. Bashkirtseva, Irina A. & Ryashko, Lev B. & Pisarchik, Alexander N., 2020. "Ring of map-based neural oscillators: From order to chaos and back," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    9. Matilla-Garcia, Mariano, 2007. "A non-parametric test for independence based on symbolic dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3889-3903, December.
    10. Mariano Matilla-García & Manuel Ruiz Marín & Mohammed Dore & Rina Ojeda, 2014. "Nonparametric correlation integral–based tests for linear and nonlinear stochastic processes," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(1), pages 181-193, April.
    11. Loretta Mastroeni & Pierluigi Vellucci, 2016. ""Butterfly Effect" vs Chaos in Energy Futures Markets," Papers 1610.05697, arXiv.org.
    12. Demos, Guilherme & Da Silva, Sergio & Matsushita, Raul, 2015. "Some Statistical Properties of the Mini Flash Crashes," MPRA Paper 65473, University Library of Munich, Germany.
    13. Vogl, Markus, 2022. "Controversy in financial chaos research and nonlinear dynamics: A short literature review," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    14. Resende, Marcelo & Zeidan, Rodrigo M., 2008. "Expectations and chaotic dynamics: Empirical evidence on exchange rates," Economics Letters, Elsevier, vol. 99(1), pages 33-35, April.
    15. Bask, Miia & Bask, Mikael, 2010. "Inequality Generating Processes and Measurement of the Matthew Effect," Working Paper Series 2010:19, Uppsala University, Department of Economics.
    16. Mikael Bask, 2024. "Skill, status and the Matthew effect: a theoretical framework," Journal of Computational Social Science, Springer, vol. 7(3), pages 2221-2253, December.
    17. repec:zbw:bofrdp:2007_020 is not listed on IDEAS
    18. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    19. Matilla-Garci­a, Mariano & Ruiz Mari­n, Manuel, 2008. "A non-parametric independence test using permutation entropy," Journal of Econometrics, Elsevier, vol. 144(1), pages 139-155, May.

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