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

  • Park, Joon Y.
  • Whang, Yoon-Jae

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.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 169 (2012)
Issue (Month): 1 ()
Pages: 61-74

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Handle: RePEc:eee:econom:v:169:y:2012:i:1:p:61-74
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Rodney C. Wolff & Qiwei Yao & Howell Tong, 2004. "Statistical tests for Lyapunov exponents of deterministic systems," LSE Research Online Documents on Economics 154, London School of Economics and Political Science, LSE Library.
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  4. Mototsugu Shintani & Oliver Linton, 2002. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," LSE Research Online Documents on Economics 2093, London School of Economics and Political Science, LSE Library.
  5. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
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  9. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
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  13. 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.
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