IDEAS home Printed from https://ideas.repec.org/p/qut/dpaper/167.html
   My bibliography  Save this paper

Statistical Tests for Lyapunov Exponents of Deterministic Systems

Author

Listed:
  • Rodney Wolff
  • Qiwei Yao
  • Howell Tong

Abstract

In order to develop statistical tests for the Lyapunov exponents of deterministic dynamical systems, we develop bootstrap tests based on empirical likelihood for percentiles and expectiles of strictly stationary processes. The percentiles and expectiles are estimated in terms of asymmetric least deviations and asymmetric least squares methods. Asymptotic distributional properties of the estimators are established.

Suggested Citation

  • Rodney Wolff & Qiwei Yao & Howell Tong, 2003. "Statistical Tests for Lyapunov Exponents of Deterministic Systems," School of Economics and Finance Discussion Papers and Working Papers Series 167, School of Economics and Finance, Queensland University of Technology.
  • Handle: RePEc:qut:dpaper:167
    as

    Download full text from publisher

    File URL: http://external-apps.qut.edu.au/business/documents/discussionPapers/2003/wolff-yao-tong.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Yao, Qiwei & Tong, Howell, 1996. "Asymmetric least squares regression estimation: a nonparametric approach," LSE Research Online Documents on Economics 19423, London School of Economics and Political Science, LSE Library.
    2. 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.
    3. Yao, Qiwei & Tong, Howell, 1998. "A bootstrap detection for operational determinism," LSE Research Online Documents on Economics 6697, London School of Economics and Political Science, LSE Library.
    4. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
    5. Yao, Qiwei & Tong, Howell, 1994. "Quantifying the influence of initial values on nonlinear prediction," LSE Research Online Documents on Economics 19426, London School of Economics and Political Science, LSE Library.
    6. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
    7. Fan, Jianqing & Yao, Qiwei & Tong, Howell, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," LSE Research Online Documents on Economics 6704, London School of Economics and Political Science, LSE Library.
    8. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Park, Joon Y. & Whang, Yoon-Jae, 2012. "Random walk or chaos: A formal test on the Lyapunov exponent," Journal of Econometrics, Elsevier, vol. 169(1), pages 61-74.

    More about this item

    Keywords

    Bootstrap; chaos; empirical likelihood; expectile; percentile.;

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:qut:dpaper:167. 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: (Angela Fletcher). General contact details of provider: http://edirc.repec.org/data/sequtau.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.