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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.

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Paper provided by FEDEA in its series Working Papers with number 2003-09.

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Handle: RePEc:fda:fdaddt:2003-09

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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, Elsevier, vol. 39(2), pages 207-211, June.
  2. William Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 2012. "A Single-Blind Controlled Competition Among Tests For Nonlinearity And Chaos," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 201219, University of Kansas, Department of Economics, revised Sep 2012.
  3. Yoon-Jae Whang & Oliver Linton, 1997. "The Asymptotic Distribution of Nonparametric Estimates of the Lyapunov Exponent for Stochastic Time Series," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1130R, Cowles Foundation for Research in Economics, Yale University.
  4. Dechert, W D & Gencay, R, 1992. "Lyapunov Exponents as a Nonparametric Diagnostic for Stability Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 7(S), pages S41-60, Suppl. De.
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