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Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos Author info | Abstract | Publisher info | Download info | Related research | Statistics Mototsugu Shintani () (Department of Economics, Vanderbilt University)
Oliver Linton () (Department of Economics, London School of Economics)
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This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the estimated Lyapunov exponents and a consistent variance estimator. A simulation study to evaluate small sample performance is reported. We also apply our procedures to daily stock return data. In most cases, the hypothesis of chaos in the stock return series is rejected at the 1% level with an exception in some higher power transformed absolute returns.
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Paper provided by Department of Economics, Vanderbilt University in its series Working Papers with number
0309.
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Date of creation: May 2003Date of revision:
Handle: RePEc:van:wpaper:0309Contact details of provider: Postal: Box 1819, Station B, Nashville, TN 37235 Fax: 615-343-8495 Email: Web page: http://sitemason.vanderbilt.edu/econ/ More information through EDIRC
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Keywords: Artificial neural networks nonlinear dynamics nonlinear time series nonparametric regression sieve estimation Other versions of this item:
Find related papers by JEL classification: C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile , click on "citations" and make appropriate adjustments.: Brock, William A. & Hommes, Cars H., 1998.
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references Cited by : (explanations , Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile , click on "citations" and make appropriate adjustments.)
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Rodney Wolff & Qiwei Yao & Howell Tong, 2004.
"Statistical Tests for Lyapunov Exponents of Deterministic Systems ,"
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