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Statistical Inference Theory for Measures of Complexity in Chaos Theory and Nonlinear Science

  • W. A. Brock
  • W. D. Dechert
Part of the NATO ASI Series book series (NSSB, volume 208)

Abstract

Concepts such as the Grassberger and Procaccia (1983a,b) correlation dimension, Kolmogorov entropy, and measures of sensitive dependence on initial conditions are making their way into economics. But they have been rather drastically modified to cope with the special issues that economic applications raise. In this paper we will survey some literature in economics that deals with these issues. In order to save space and concentrate on what we know best we will focus on our own work. Citations will be given to help the reader locate the work of others. First we will take up the question of testing for low dimensional deterministic chaos in economics and finance where the vast bulk of professional belief is centered on nonstationary and stochastic data. Second, in Section 2 we will deal with some of the technical underpinnings of the methodology we discuss in Section 1. Third, in Section 3, we briefly mention applications and take up unresolved issues not covered in Sections 1 and 2.

Keywords

Stock Return Large Lyapunov Exponent Asymptotic Standard Error Small Sample Property Kolmogorov Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • W. A. Brock
    • 1
    • 2
  • W. D. Dechert
    • 1
    • 2
  1. 1.Dept. of EconomicsUniversity of WisconsinMadisonUSA
  2. 2.Dept. of EconomicsUniversity of HoustonHoustonUSA

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