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The Asymptotic Distribution of Nonparametric Estimates of the Lyapunov Exponent for Stochastic Time Series

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Author Info
Yoon-Jae Whang (Ewha University & Yale University)
Oliver Linton (Cowles Foundation, Yale University)

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Abstract

This paper derives the asymptotic distribution of a smoothing-based estimator of the Lyapunov exponent for a stochastic time series under two general scenarios. In the first case, we are able to establish root-T consistency and asymptotic normality, while in the second case, which is more relevant for chaotic processes, we are only able to establish asymptotic normality at a slower rate of convergence. We provide consistent confidence intervals for both cases. We apply our procedures to simulated data.

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File URL: http://cowles.econ.yale.edu/P/cd/d11a/d1130-r.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1130R.

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Length: 47 pages
Date of creation: Oct 1997
Date of revision:
Handle: RePEc:cwl:cwldpp:1130r

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Chaos; kernel; nonlinear dynamics; nonparametric regression; semiparametric;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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  1. Oliver Linton & Mototsugu Shintani, 2002. "Nonparametric Neutral Network Estimation of Lyapunov Exponents and a Direct Test for Chaos," STICERD - Econometrics Paper Series /2002/434, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  2. Rodney Wolff & Qiwei Yao & Howell Tong, 2003. "Statistical Tests for Lyapunov Exponents of Deterministic Systems," School of Economics and Finance Discussion Papers and Working Papers Series 167, School of Economics and Finance, Queensland University of Technology. [Downloadable!]
  3. Simón Sosvilla-Rivero & Fernando Fernández-Rodriguez & Julián Andrada-Félix, 2005. "Testing chaotic dynamics via Lyapunov exponents," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 911-930. [Downloadable!]
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  4. Rodney C Wolff & Qiwei Yao & Howell Tong, 2006. "Statistical tests for Lyapunov exponents of deterministic systems," Rodney Wolff Papers 2006-8, School of Economics and Finance, Queensland University of Technology. [Downloadable!]
  5. Joon Y. Park & Yoon-Jae Whang, 1999. "Random Walk or Chaos: A Formal Test on the Lyapunov Exponent," Working Paper Series no9, Institute of Economic Research, Seoul National University. [Downloadable!]
  6. Mototsugu Shintani & Oliver Linton, 2000. "Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors," Working Papers 0111, Department of Economics, Vanderbilt University, revised Jun 2001. [Downloadable!]
    Other versions:
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