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Dynamical Models of Stock Prices Based on Technical Trading Rules Part II: Analysis of the Models

  • Li-Xin Wang
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    In Part II of this paper, we concentrate our analysis on the price dynamical model with the moving average rules developed in Part I of this paper. By decomposing the excessive demand function, we reveal that it is the interplay between trend-following and contrarian actions that generates the price chaos, and give parameter ranges for the price series to change from divergence to chaos and to oscillation. We prove that the price dynamical model has an infinite number of equilibrium points but all these equilibrium points are unstable. We demonstrate the short-term predictability of the return volatility and derive the detailed formula of the Lyapunov exponent as function of the model parameters. We show that although the price is chaotic, the volatility converges to some constant very quickly at the rate of the Lyapunov exponent. We extract the formula relating the converged volatility to the model parameters based on Monte-Carlo simulations. We explore the circumstances under which the returns show independency and illustrate in details how the independency index changes with the model parameters. Finally, we plot the strange attractor and return distribution of the chaotic price model to illustrate the complex structure and fat-tailed distribution of the returns.

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    File URL: http://arxiv.org/pdf/1401.1891
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    Paper provided by arXiv.org in its series Papers with number 1401.1891.

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    Date of creation: Jan 2014
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    Handle: RePEc:arx:papers:1401.1891
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    1. Andrew W. Lo & Harry Mamaysky & Jiang Wang, 2000. "Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation," NBER Working Papers 7613, National Bureau of Economic Research, Inc.
    2. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: II. Agent-based models," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1013-1041.
    3. Tesfatsion, Leigh & Judd, Kenneth L., 2006. "Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics," Staff General Research Papers 10368, Iowa State University, Department of Economics.
    4. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    5. Amit Goyal & Ivo Welch, 2004. "A Comprehensive Look at the Empirical Performance of Equity Premium Prediction," Yale School of Management Working Papers amz2412, Yale School of Management, revised 01 Jan 2006.
    6. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    7. Menkhoff, Lukas, 2010. "The use of technical analysis by fund managers: International evidence," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2573-2586, November.
    8. Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-77, December.
    9. Andrei A. Kirilenko & Andrew W. Lo, 2013. "Moore's Law versus Murphy's Law: Algorithmic Trading and Its Discontents," Journal of Economic Perspectives, American Economic Association, vol. 27(2), pages 51-72, Spring.
    10. Kirman, Alan, 1989. "The Intrinsic Limits of Modern Economic Theory: The Emperor Has No Clothes," Economic Journal, Royal Economic Society, vol. 99(395), pages 126-39, Supplemen.
    11. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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