Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos
AbstractThis 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 120 (2004)
Issue (Month): 1 (May)
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Web page: http://www.elsevier.com/locate/jeconom
Other versions of this item:
- Oliver Linton & Mototsugu Shintani, 2002. "Nonparametric Neutral Network Estimation of Lyapunov Exponents and a Direct Test for Chaos," STICERD - Econometrics Paper Series /2002/434, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Mototsugu Shintani & Oliver Linton, 2003. "Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos," Vanderbilt University Department of Economics Working Papers 0309, Vanderbilt University Department of Economics.
- Oliver Linton & Mototsugu Shintani, 2003. "Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos," STICERD - Econometrics Paper Series /2003/455, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- 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 &bull Diffusion Processes
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- 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.
- Yoon-Jae Whang & Oliver Linton, 1997. "The Asymptotic Distribution of Nonparametric Estimates of the Lyapunov Exponent for Stochastic Time Series," Cowles Foundation Discussion Papers 1130R, Cowles Foundation for Research in Economics, Yale University.
- Abhyankar, A & Copeland, L S & Wong, W, 1997. "Uncovering Nonlinear Structure in Real-Time Stock-Market Indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 1-14, January.
- Gencay Ramazan & Dechert W. Davis, 1996. "The Identification of Spurious Lyapunov Exponents in Jacobian Algorithms," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(3), pages 1-12, October.
- William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 1996.
"A Single-Blind Controlled Competition among Tests for Nonlinearity and Chaos,"
9602005, EconWPA, revised 20 Sep 1996.
- Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997. "A single-blind controlled competition among tests for nonlinearity and chaos," Journal of Econometrics, Elsevier, vol. 82(1), pages 157-192.
- William Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 2012. "A Single-Blind Controlled Competition Among Tests For Nonlinearity And Chaos," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201219, University of Kansas, Department of Economics, revised Sep 2012.
- Brock, William A. & Hommes, Cars H., 1998.
"Heterogeneous beliefs and routes to chaos in a simple asset pricing model,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 22(8-9), pages 1235-1274, August.
- Donald W.K. Andrews, 1988.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Cowles Foundation Discussion Papers
877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
- Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
- Serletis, Apostolos, 1995. "Random Walks, Breaking Trend Functions, and the Chaotic Structure of the Velocity of Money," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 453-58, October.
- Bask, Mikael & de Luna, Xavier, 2001.
"Characterizing the degree of stability of non-linear dynamic models,"
UmeÃ¥ Economic Studies
564, Umeå University, Department of Economics.
- Bask Mikael & de Luna Xavier, 2002. "Characterizing the Degree of Stability of Non-linear Dynamic Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(1), pages 1-19, April.
- 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 S41-60, Suppl. De.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
- Barnett,William A. & Kirman,Alan P. & Salmon,Mark, 1997. "Nonlinear Dynamics and Economics," Cambridge Books, Cambridge University Press, number 9780521471411, December.
- 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.
- Oliver Linton & Mototsugu Shintani, 2001. "Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors," FMG Discussion Papers dp383, Financial Markets Group.
- Mototsugu Shintani & Oliver Linton, 2001. "Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors," Vanderbilt University Department of Economics Working Papers 0111, Vanderbilt University Department of Economics.
- Barnett, William A. & Ronald Gallant, A. & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1995. "Robustness of nonlinearity and chaos tests to measurement error, inference method, and sample size," Journal of Economic Behavior & Organization, Elsevier, vol. 27(2), pages 301-320, July.
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