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The Chaotic Attractor Analysis of DJIA Based on Manifold Embedding and Laplacian Eigenmaps

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  • Xiaohua Song
  • Dongxiao Niu
  • Yulin Zhang

Abstract

By using the techniques of Manifold Embedding and Laplacian Eigenmaps, a novel strategy has been proposed in this paper to detect the chaos of Dow Jones Industrial Average. Firstly, the chaotic attractor of financial time series is assumed to lie on a low-dimensional manifold that is embedded into a high-dimensional Euclidean space. Then, an improved phase space reconstruction method and a nonlinear dimensionality reduction method are introduced to help reveal the structure of the chaotic attractor. Next, the empirical study on the financial time series of Dow Jones Industrial Average shows that there exists an attractor which lies on a manifold constructed by the time sequence of Moving average convergence divergence; finally, Determinism Test, Poincaré section, and translation analysis are used as test approaches to prove both whether it is a chaos and how it works.

Suggested Citation

  • Xiaohua Song & Dongxiao Niu & Yulin Zhang, 2016. "The Chaotic Attractor Analysis of DJIA Based on Manifold Embedding and Laplacian Eigenmaps," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-10, June.
  • Handle: RePEc:hin:jnlmpe:8087178
    DOI: 10.1155/2016/8087178
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    Cited by:

    1. Vogl, Markus, 2022. "Controversy in financial chaos research and nonlinear dynamics: A short literature review," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Monia ANTAR, 2016. "Autosimilarité et mémoire longue : Les rendements des indices boursiers tunisiens sont-ils chaotiques ?," Journal of Academic Finance, RED research unit, university of Gabes, Tunisia, vol. 7(2), pages 1-32, November.
    3. Vogl, Markus & Kojić, Milena & Mitić, Petar, 2024. "Dynamics of green and conventional bond markets: Evidence from the generalized chaos analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).

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