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

Joon Y. Park and Yoon-Jae Whang

Journal of Econometrics, 2012, vol. 169, issue 1, 61-74

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.

Keywords: Lyapunov exponent; Chaos; Random walk; Unit root; Kernel regression; Brownian motion; Local time; Stochastic integrals (search for similar items in EconPapers)
JEL-codes: C14 C22 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:169:y:2012:i:1:p:61-74

DOI: 10.1016/j.jeconom.2012.01.012

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