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Testing Chaotic Dynamics via Lyapunov Exponents

Listed author(s):
  • Fernando Fernández-Rodríguez
  • Simón Sosvilla-Rivero
  • Julián Andrada-Félix

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.

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File URL: http://documentos.fedea.net/pubs/dt/2000/dt-2000-07.pdf
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Paper provided by FEDEA in its series Working Papers with number 2000-07.

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Handle: RePEc:fda:fdaddt:2000-07
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  1. Mayfield, E Scott & Mizrach, Bruce, 1992. "On Determining the Dimension of Real-Time Stock-Price Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 367-374, July.
  2. 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.
  3. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-337, July.
  4. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
  5. Oliver Linton & Mototsugu Shintani, 2001. "Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors," FMG Discussion Papers dp383, Financial Markets Group.
  6. 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.
  7. Bask , Mikael, 1997. "Deterministic Chaos in Exchange Rates?," Umeå Economic Studies 453, Umeå University, Department of Economics.
  8. Yoon-Jae Whang & Oliver Linton, 1997. "The Asymptotic Distribution of Nonparametric Estimates of the Lyapunov Exponent for Stochastic Time Series," Cowles Foundation Discussion Papers 1130R, Cowles Foundation for Research in Economics, Yale University.
  9. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  10. Gencay Ramazan & Dechert W. Davis, 1996. "The Identification of Spurious Lyapunov Exponents in Jacobian Algorithms," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(3), pages 1-12, October.
  11. 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.
  12. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  13. Sergio Da Silva, 2001. "Chaotic Exchange Rate Dynamics Redux," Open Economies Review, Springer, vol. 12(3), pages 281-304, July.
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