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Testing Chaotic Dynamics via Lyapunov Exponents

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Author Info
Fernando Fernández-Rodríguez
Simón Sosvilla-Rivero
Julián Andrada-Félix

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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. 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 367-74, July.
  2. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May. [Downloadable!] (restricted)
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  3. Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero & Julián Andrada-Félix, . "A New Test for Chaotic Dynamics Using Lyapunov Exponents," Working Papers 2003-09, FEDEA. [Downloadable!]
  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, vol. 82(1), pages 157-192. [Downloadable!] (restricted)
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  5. Mototsugu Shintani & Oliver Linton, 2003. "Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(1), pages 331-357, February. [Downloadable!] (restricted)
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  6. Sergio Da Silva, 2001. "Chaotic Exchange Rate Dynamics Redux," Open Economies Review, Springer, vol. 12(3), pages 281-304, July. [Downloadable!] (restricted)
  7. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," Journal of Business, University of Chicago Press, vol. 62(3), pages 311-37, July. [Downloadable!] (restricted)
  8. Ramazan Gencay & W. Davis Dechert, 1996. "The Identification of Spurious Lyapunov Exponents in Jacobian Algorithms," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 1(3). [Downloadable!]
  9. 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. [Downloadable!] (restricted)
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  10. 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. [Downloadable!] (restricted)
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  1. José Julián Escario & José Alberto Molina, . "Do tobacco taxes reduce lung cancer mortality?," Working Papers 2000-17, FEDEA. [Downloadable!]
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