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Is the German Stock Market Chaotic ? Some NEGM- and BDS-test results for the DAX

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  • Oliver Moritz

    (University of Mainz)

Abstract

The NEGM (Nychka, Ellner, Gallant, MacCaffrey)-test for a positive largest Lyapunov-Exponent via neural nets (NN) led to new interest in testing economic time series for chaos. This is mainly due to two reasons: First, their different concept of chaos, admitting stochastic nonlinear systems to be chaotic too, is more applicable to real economic time series. Second, neural nets seem to bear reliable results even for very noisy systems. The drawback of the algorithm is, that it is very time consuming because of multiple local minima and the ill-conditioned nature of NN-fitting. Using a sparser net topologie, replacing one hidden unit by so called shortcut connections, can improve the accuracy in many cases. We use this topologie to estimate the dominant Lyapunov-Exponent for the DAX (Deutscher Aktienindex) from 1988 to 1996. In this period the german stock market didn't seem to be chaotic - even in the week stochastic sense. Furthermore an inspection of the residuals with the BDS (Brock, Dechert, Scheinkmann)-test shows that the apparent nonlinearity in the data can't be explained by a nonlinear model with additive noise.

Suggested Citation

  • Oliver Moritz, 2001. "Is the German Stock Market Chaotic ? Some NEGM- and BDS-test results for the DAX," CeNDEF Workshop Papers, January 2001 3A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    • Handle: RePEc:ams:cdws01:3a.2
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    References listed on IDEAS

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    1. 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.
    2. Abhyankar, A & Copeland, L S & Wong, W, 1997. "Uncovering Nonlinear Structure in Real-Time Stock-Market Indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 1-14, January.
    3. William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan, 2004. "A Single-Blind Controlled Competition Among Tests for Nonlinearity and Chaos," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 581-615, Emerald Group Publishing Limited.
    4. Brock, W. A., 1986. "Distinguishing random and deterministic systems: Abridged version," Journal of Economic Theory, Elsevier, vol. 40(1), pages 168-195, October.
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