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A New Test for Chaotic Dynamics Using Lyapunov Exponents

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

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 nonlinearity and chaos that were generated by Barnett et al. (1997), as well as to several chaotic series. The results suggest that the new test is particularly effective when compared to other stochastic alternatives (both linear and nonlinear). The test size is one for large samples, although for small sample sizes it diminishes below the nominal size for two out of the three chaotic processes considered, what is not a surprise given some well-known properties of such processes.

Suggested Citation

  • Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero & Julián Andrada-Félix, "undated". "A New Test for Chaotic Dynamics Using Lyapunov Exponents," Working Papers 2003-09, FEDEA.
  • Handle: RePEc:fda:fdaddt:2003-09
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    References listed on IDEAS

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    1. Bajo-Rubio, Oscar & Fernandez-Rodriguez, Fernando & Sosvilla-Rivero, Simon, 1992. "Chaotic behaviour in exchange-rate series : First results for the Peseta--U.S. dollar case," Economics Letters, Elsevier, vol. 39(2), pages 207-211, June.
    2. Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997. "A single-blind controlled competition among tests for nonlinearity and chaos," Journal of Econometrics, Elsevier, vol. 82(1), pages 157-192.
    3. Dechert, W D & Gencay, R, 1992. "Lyapunov Exponents as a Nonparametric Diagnostic for Stability Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 41-60, Suppl. De.
    4. Whang, Yoon-Jae & Linton, Oliver, 1999. "The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series," Journal of Econometrics, Elsevier, vol. 91(1), pages 1-42, July.
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