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Testing Chaotic Dynamics via Lyapunov Exponents

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  • Fernando Fernández-Rodríguez
  • Simón Sosvilla-Rivero
  • Julián Andrada-Félix

Abstract

In this paper, we propose a new test, based on the stability of the largest Lyapunov exponent from different sample sizes, to detect chaotic dynamics in economic and financial time series. We apply this new test to the simulated data used in the single-blind controlled competition among tests for for nonlinearity and chaos provided by Barnet et al. (1997), both for small samples (380 observations) and for large samples (2000 observations). The results suggest that the new test has high power against different stochastic alternatives (both linear and nonlinear) and that behaves well in small samples.

Suggested Citation

  • Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero & Julián Andrada-Félix, "undated". "Testing Chaotic Dynamics via Lyapunov Exponents," Working Papers 2000-07, FEDEA.
    • Handle: RePEc:fda:fdaddt:2000-07
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    Cited by:

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    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. Vogl, Markus, 2022. "Controversy in financial chaos research and nonlinear dynamics: A short literature review," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    6. 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.
    7. 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.
    8. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    9. 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.
    10. 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).
    11. Bask, Miia & Bask, Mikael, 2010. "Inequality Generating Processes and Measurement of the Matthew Effect," Working Paper Series 2010:19, Uppsala University, Department of Economics.
    12. 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.
    13. 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.
    14. repec:zbw:bofrdp:2007_020 is not listed on IDEAS
    15. 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.
    16. Loretta Mastroeni & Pierluigi Vellucci, 2016. ""Butterfly Effect" vs Chaos in Energy Futures Markets," Papers 1610.05697, arXiv.org.
    17. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    18. 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.
    19. Demos, Guilherme & Da Silva, Sergio & Matsushita, Raul, 2015. "Some Statistical Properties of the Mini Flash Crashes," MPRA Paper 65473, University Library of Munich, Germany.

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