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Some Theory of Statistical Inference for Nonlinear Science

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  • William A. Brock
  • Ehung G. Baek

Abstract

This article shows how standard errors can be estimated for a measure of the number of excited degrees of freedom (the correlation dimension), and a measure of the rate of information creation (a proxy for the Kolmogorov entropy), and a measure of instability. These measures are motivated by nonlinear science and chaos theory. The main analytical method is central limit theory of U-statistics for mixing processes. The paper takes a step toward formal hypothesis testing in nonlinear science and chaos theory.

Suggested Citation

  • William A. Brock & Ehung G. Baek, 1991. "Some Theory of Statistical Inference for Nonlinear Science," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(4), pages 697-716.
    • Handle: RePEc:oup:restud:v:58:y:1991:i:4:p:697-716.
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    File URL: http://hdl.handle.net/10.2307/2297828
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    Cited by:

    1. Antonios Antoniou & Constantinos E. Vorlow, 2004. "Price Clustering and Discreteness: Is there Chaos behind the Noise?," Papers cond-mat/0407471, arXiv.org.
    2. Per Bjarte Solibakke, 2003. "Validity of discrete-time stochastic volatility models in non-synchronous equity markets," The European Journal of Finance, Taylor & Francis Journals, vol. 9(5), pages 420-448.
    3. Mills, Terence C., 1995. "Business cycle asymmetries and non-linearities in U.K. macroeconomic time series," Ricerche Economiche, Elsevier, vol. 49(2), pages 97-124, June.
    4. Constantinos E. Vorlow, 2004. "Stock Price Clustering and Discreteness: The "Compass Rose" and Predictability," Papers cond-mat/0408013, arXiv.org.
    5. Guoxiang Xu & Wangfeng Gao, 2019. "Financial Risk Contagion in Stock Markets: Causality and Measurement Aspects," Sustainability, MDPI, vol. 11(5), pages 1-20, March.
    6. Ignacio Olmeda & Joaquin Pérez, 1995. "Non-linear dynamics and chaos in the Spanish stock market," Investigaciones Economicas, Fundación SEPI, vol. 19(2), pages 217-248, May.
    7. Antoniou, Antonios & Vorlow, Constantinos E., 2005. "Price clustering and discreteness: is there chaos behind the noise?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 389-403.
    8. Mayer-Foulkes, David, 1995. "A statistical correlation dimension," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 277-293, September.
    9. McKenzie, Michael D., 2001. "Chaotic behavior in national stock market indices: New evidence from the close returns test," Global Finance Journal, Elsevier, vol. 12(1), pages 35-53.
    10. Mizrach, Bruce, 1996. "Determining delay times for phase space reconstruction with application to the FF/DM exchange rate," Journal of Economic Behavior & Organization, Elsevier, vol. 30(3), pages 369-381, September.

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