Testing chaotic dynamics via Lyapunov exponents
We propose a new test to detect chaotic dynamics, based on the stability of the largest Lyapunov exponent from different sample sizes. This test is applied to the data used in the single-blind controlled competition tests for non-linearity and chaos that were generated by Barnett et al. (1997), as well as to several other chaotic series. The results suggest that the new test is particularly effective when compared to other stochastic alternatives (both linear and non-linear). For large sample sizes the power of the test is one, although for small sample sizes it diminishes occasionally. Copyright © 2005 John Wiley & Sons, Ltd.
Volume (Year): 20 (2005)
Issue (Month): 7 ()
|Contact details of provider:|| Web page: http://www.interscience.wiley.com/jpages/0883-7252/|
|Order Information:|| Web: http://www3.interscience.wiley.com/jcatalog/subscribe.jsp?issn=0883-7252 Email: |
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.:
- 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.
- Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-37, July.
- 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.
- Bajo-Rubio, Oscar & Fernandez-Rodriguez, Fernando & Sosvilla-Rivero, Simon, 1992. "Chaotic behaviour in exchange-rate series : First results for the Peseta--U.S. dollar case," Economics Letters, Elsevier, vol. 39(2), pages 207-211, June.
- 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.
- 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.
- Bask , Mikael, 1997. "Deterministic Chaos in Exchange Rates?," Umeå Economic Studies 453, Umeå University, Department of Economics.
- 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.
- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- 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.
- 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.
- 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.
- 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.
- 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," Econometrics 9602005, EconWPA, revised 20 Sep 1996.
- Newey, Whitney & West, Kenneth, 2014.
"A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix,"
Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
- Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
- Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
- Mayfield, E Scott & Mizrach, Bruce, 1992. "On Determining the Dimension of Real-Time Stock-Price Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 367-74, July.
- Sergio Da Silva, 2001. "Chaotic Exchange Rate Dynamics Redux," Open Economies Review, Springer, vol. 12(3), pages 281-304, July.
When requesting a correction, please mention this item's handle: RePEc:jae:japmet:v:20:y:2005:i:7:p:911-930. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing)or (Christopher F. Baum)
If references are entirely missing, you can add them using this form.