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Random walk or chaos: A formal test on the Lyapunov exponent

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  • Park, Joon Y.
  • Whang, Yoon-Jae

Abstract

A formal test on the Lyapunov exponent is developed to distinguish a random walk model from a chaotic system, which is based on the Nadaraya–Watson kernel estimator of the Lyapunov exponent. The asymptotic null distribution of our test statistic is free of nuisance parameter, and simply given by the range of standard Brownian motion on the unit interval. The test is consistent against the chaotic alternatives. A simulation study shows that the test performs reasonably well in finite samples. We apply our test to some of the standard macro and financial time series, finding no significant empirical evidence of chaos.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:169:y:2012:i:1:p:61-74
    DOI: 10.1016/j.jeconom.2012.01.012
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    Cited by:

    1. Arturo Lorenzo Valdés, 2002. "Pruebas de no linealidad de los rendimientos del mercado mexicano accionario: coeficientes de Lyapunov," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 17(2), pages 305-322.
    2. Domowitz, Ian & El-Gamal, Mahmoud A., 2001. "A consistent nonparametric test of ergodicity for time series with applications," Journal of Econometrics, Elsevier, vol. 102(2), pages 365-398, June.
    3. 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.
    4. Giannerini Simone & Rosa Rodolfo, 2004. "Assessing Chaos in Time Series: Statistical Aspects and Perspectives," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-25, May.

    More about this item

    Keywords

    Lyapunov exponent; Chaos; Random walk; Unit root; Kernel regression; Brownian motion; Local time; Stochastic integrals;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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