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Lyapunov Exponents as a Nonparametric Diagnostic for Stability Analysis

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  • Dechert, W D
  • Gencay, R

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.

Suggested Citation

  • Dechert, W D & Gencay, R, 1992. "Lyapunov Exponents as a Nonparametric Diagnostic for Stability Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 41-60, Suppl. De.
  • Handle: RePEc:jae:japmet:v:7:y:1992:i:s:p:s41-60
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    Cited by:

    1. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
    2. repec:kap:iaecre:v:3:y:1997:i:2:p:142-153 is not listed on IDEAS
    3. Park, Joon Y. & Whang, Yoon-Jae, 2012. "Random walk or chaos: A formal test on the Lyapunov exponent," Journal of Econometrics, Elsevier, vol. 169(1), pages 61-74.
    4. Bask, Mikael & Liu, Tung & Widerberg, Anna, 2006. "The stability of electricity prices : estimation and inference of the Lyapunov exponents," Research Discussion Papers 9/2006, Bank of Finland.
    5. Raphael Markellos & Costas Siriopoulos, 1997. "Diversification benefits in the smaller European stock markets," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 3(2), pages 142-153, May.
    6. Bask, Miia & Bask, Mikael, 2014. "Social influence and the Matthew mechanism: The case of an artificial cultural market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 113-119.
    7. repec:eee:ecofin:v:42:y:2017:i:c:p:584-596 is not listed on IDEAS
    8. 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.
    9. Arifovic, Jasmina & Gençay, Ramazan, 2001. "Using genetic algorithms to select architecture of a feedforward artificial neural network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(3), pages 574-594.
    10. Shintani, Mototsugu, 2008. "A dynamic factor approach to nonlinear stability analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2788-2808, September.
    11. 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.
    12. Elena Olmedo & Ricardo Gimeno & Lorenzo Escot & Ruth Mateos, 2007. "Convergencia y Estabilidad de los Tipos de Cambio Europeos: Una Aplicación de Exponentes de Lyapunov," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 44(129), pages 91-108.
    13. 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.
    14. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    15. Arifovic, Jasmina & Gencay, Ramazan, 2000. "Statistical properties of genetic learning in a model of exchange rate," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 981-1005, June.
    16. Bask, Mikael & Liu, Tung & Widerberg, Anna, 2007. "The stability of electricity prices: Estimation and inference of the Lyapunov exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 565-572.
    17. Haim H. Bau & Yochanan Shachmurove, 2002. "Chaos Theory And Its Application," Penn CARESS Working Papers 6a7863cdd8e575c9e635b060c, Penn Economics Department.
    18. Bask, Mikael, 2007. "Measuring potential market risk," Research Discussion Papers 20/2007, Bank of Finland.
    19. Anagnostidis, Panagiotis & Emmanouilides, Christos J., 2015. "Nonlinearity in high-frequency stock returns: Evidence from the Athens Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 473-487.
    20. Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero & Julián Andrada-Félix, "undated". "A New Test for Chaotic Dynamics Using Lyapunov Exponents," Working Papers 2003-09, FEDEA.

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