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Testing Chaotic Dynamics via Lyapunov Exponents

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

Abstract

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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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. Mototsugu Shintani & Oliver Linton, 2001. "Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors," Vanderbilt University Department of Economics Working Papers, Vanderbilt University Department of Economics 0111, Vanderbilt University Department of Economics.
  2. Bask , Mikael, 1997. "Deterministic Chaos in Exchange Rates?," UmeÃ¥ Economic Studies, UmeÃ¥ University, Department of Economics 453, Umeå University, Department of Economics.
  3. 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, Elsevier, vol. 52(1-2), pages 5-59.
  4. 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, Elsevier, vol. 82(1), pages 157-192.
  5. 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.
  6. Sergio Da Silva, 2001. "Chaotic Exchange Rate Dynamics Redux," Open Economies Review, Springer, Springer, vol. 12(3), pages 281-304, July.
  7. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0055, National Bureau of Economic Research, Inc.
  8. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 62(3), pages 311-37, July.
  9. 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.
  10. 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.
  11. 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, Elsevier, vol. 1(1), pages 83-106, June.
  12. Mayfield, E Scott & Mizrach, Bruce, 1992. "On Determining the Dimension of Real-Time Stock-Price Data," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 10(3), pages 367-74, July.
  13. Gencay Ramazan & Dechert W. Davis, 1996. "The Identification of Spurious Lyapunov Exponents in Jacobian Algorithms," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 1(3), pages 1-12, October.
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Cited by:
  1. Park, Joon Y. & Whang, Yoon-Jae, 2012. "Random walk or chaos: A formal test on the Lyapunov exponent," Journal of Econometrics, Elsevier, Elsevier, vol. 169(1), pages 61-74.
  2. Matilla-Garcia, Mariano, 2007. "A non-parametric test for independence based on symbolic dynamics," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 31(12), pages 3889-3903, December.
  3. Bask, Mikael & Widerberg, Anna, 2009. "Market structure and the stability and volatility of electricity prices," Energy Economics, Elsevier, Elsevier, vol. 31(2), pages 278-288, March.
  4. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, Elsevier, vol. 6(3), pages 180-186, September.
  5. Matilla-García, Mariano & Marín, Manuel Ruiz, 2010. "A new test for chaos and determinism based on symbolic dynamics," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 76(3), pages 600-614, December.
  6. Mariano Matilla-García & Manuel Ruiz Marín & Mohammed Dore & Rina Ojeda, 2014. "Nonparametric correlation integral–based tests for linear and nonlinear stochastic processes," Decisions in Economics and Finance, Springer, Springer, vol. 37(1), pages 181-193, April.
  7. Matilla-Garci­a, Mariano & Ruiz Mari­n, Manuel, 2008. "A non-parametric independence test using permutation entropy," Journal of Econometrics, Elsevier, Elsevier, vol. 144(1), pages 139-155, May.
  8. Resende, Marcelo & Zeidan, Rodrigo M., 2008. "Expectations and chaotic dynamics: Empirical evidence on exchange rates," Economics Letters, Elsevier, Elsevier, vol. 99(1), pages 33-35, April.
  9. Bask, Miia & Bask, Mikael, 2010. "Inequality Generating Processes and Measurement of the Matthew Effect," Working Paper Series, Uppsala University, Department of Economics 2010:19, Uppsala University, Department of Economics.

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