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Lyapunov Exponents as a Nonparametric Diagnostic for Stability Analysis

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Author Info
Dechert, W D
Gencay, R

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Abstract

The common observation made in the empirical nonlinear dynamics literature is the constraints imposed by the availability of a limited number of observations in the implementation of the existing algorithms of Lyapunov exponents. The algorithm discussed here can estimate all "n" Lyapunov exponents of an unknown "n"-dimensional dynamical system accurately with limited number of observations. This makes the algorithm attractive for applications to economic as well as financial time-series data. The implementation of the algorithm is carried out by multilayer feed forward networks which are capable of approximating any function and its derivatives to any degree of accuracy. Copyright 1992 by John Wiley & Sons, Ltd.

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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 7 (1992)
Issue (Month): S (Suppl. Dec.)
Pages: S41-60
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Handle: RePEc:jae:japmet:v:7:y:1992:i:s:p:s41-60

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  1. Elena Olmedo & Ricardo Gimeno & Lorenzo Escot & Ruth Mateos, 2007. "Convergencia y Estabilidad de los Tipos de Cambio Europeos: Una Aplicación de Exponentes de Lyapunov," Cuadernos de Economía (Latin American Journal of Economics), Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 44(129), pages 91-108. [Downloadable!]
  2. 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!]
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  3. Mototsugu Shintani, 2004. "A Dynamic Factor Approach to Nonlinear Stability Analysis," Working Papers 0418, Department of Economics, Vanderbilt University. [Downloadable!]
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  4. Haim H. Bau & Yochanan Shachmurove, 2002. "Chaos Theory And Its Application," Penn CARESS Working Papers 6a7863cdd8e575c9e635b060c, Penn Economics Department. [Downloadable!]
  5. Mikael Bask & Tung Liu & Anna Widerberg, 2006. "The Stability of Electricity Prices: Estimation and Inference of the Lyapunov Exponent," Working Papers 200603, Ball State University, Department of Economics, revised Apr 2006. [Downloadable!]
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  6. 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!]
  7. 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!]
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