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Some Theory of Statistical Inference for Nonlinear Science

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  • Brock, William A
  • Baek, Ehung G

Abstract

This article shows how standard errors can be estimated for a measure of the number of excited degrees of freedom (the correlation dimension), 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. Copyright 1991 by The Review of Economic Studies Limited.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Review of Economic Studies.

Volume (Year): 58 (1991)
Issue (Month): 4 (July)
Pages: 697-716

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Handle: RePEc:bla:restud:v:58:y:1991:i:4:p:697-716

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Cited by:
  1. 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.
  2. Mayer-Foulkes, David, 1995. "A statistical correlation dimension," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 277-293, September.
  3. Antonios Antoniou & Constantinos E. Vorlow, 2004. "Price Clustering and Discreteness: Is there Chaos behind the Noise?," Papers cond-mat/0407471, arXiv.org.
  4. 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.
  5. 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.
  6. 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.
  7. Constantinos E. Vorlow, 2004. "Stock Price Clustering and Discreteness: The "Compass Rose" and Predictability," Papers cond-mat/0408013, arXiv.org.

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