A New Test for Chaotic Dynamics Using Lyapunov Exponents

FEDEA Working Paper No. 2003-09

40 Pages Posted: 5 May 2003  

Fernando Fernández Rodríguez

University of Las Palmas de Gran Canaria - Faculty of Economic Science

Simon Sosvilla-Rivero

Complutense Institute for International Studies

Julián Andrada Félix

University of Las Palmas de Gran Canaria - Faculty of Economic Science

Date Written: March 2003

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.

Keywords: Chaos, Nonlinear Dynamics, Lyapunov exponents, Bootstrapping

JEL Classification: C13, C14, C15, C22

Suggested Citation

Fernández Rodríguez, Fernando and Sosvilla-Rivero, Simon and Andrada Félix, Julián, A New Test for Chaotic Dynamics Using Lyapunov Exponents (March 2003). FEDEA Working Paper No. 2003-09. Available at SSRN: https://ssrn.com/abstract=390380 or http://dx.doi.org/10.2139/ssrn.390380

Fernando Fernández Rodríguez

University of Las Palmas de Gran Canaria - Faculty of Economic Science ( email )

Campus de Tafira
E-35017 Las Palmas
Spain
+34 928 45 18 02 (Phone)
+34 928 45 18 29 (Fax)

Simon Sosvilla-Rivero (Contact Author)

Complutense Institute for International Studies ( email )

Carretera de Humera s/n
Madrid, Madrid 28223
Spain
+34913932626 (Phone)

HOME PAGE: http://www.ucm.es/info/ecocuan/ssr/

Julián Andrada Félix

University of Las Palmas de Gran Canaria - Faculty of Economic Science ( email )

E-35017 Las Palmas
Spain
+34 928 45 59 89 (Phone)
+34 928 45 18 29 (Fax)

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