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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. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    3. William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan, 2004. "A Single-Blind Controlled Competition Among Tests for Nonlinearity and Chaos," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 581-615, Emerald Group Publishing Limited.
    4. 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.
    5. 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.
    6. Melvin J. Hinich, 1982. "Testing For Gaussianity And Linearity Of A Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 169-176, May.
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    Cited by:

    1. Simón Sosvilla Rivero & Oscar Bajo Rubio & Carmen Díaz Roldán, "undated". "Sobre la efectividad de la política regional comunitaria: El caso de Castilla-la Mancha," Studies on the Spanish Economy 178, FEDEA.
    2. 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.
    3. Juan Prieto & Juan Gabriel Rodríguez & Rafael Salas, "undated". "Polarization, Inequality and Tax Reforms," Working Papers 2003-23, FEDEA.

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