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Testing chaotic dynamics via Lyapunov exponents

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Author Info
Simón Sosvilla-Rivero (FEDEA and Universidad Complutense de Madrid, Spain)
Fernando Fernández-Rodriguez (Department of Quantitative Methods in Economics and Management, Universidad de Las Palmas de Gran Canaria, Spain)
Julián Andrada-Félix (Department of Quantitative Methods in Economics and Management, Universidad de Las Palmas de Gran Canaria, Spain)

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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 non-linearity and chaos that were generated by Barnett et al. (1997), as well as to several other chaotic series. The results suggest that the new test is particularly effective when compared to other stochastic alternatives (both linear and non-linear). For large sample sizes the power of the test is one, although for small sample sizes it diminishes occasionally. Copyright © 2005 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.805
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File URL: http://qed.econ.queensu.ca:80/jae/2005-v20.7/
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Publisher Info
Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 20 (2005)
Issue (Month): 7 ()
Pages: 911-930
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Handle: RePEc:jae:japmet:v:20:y:2005:i:7:p:911-930

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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. repec:bep:sndecm:1:1996:3:145-154 is not listed on IDEAS
  8. 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)
  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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