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Dynamical Models of Stock Prices Based on Technical Trading Rules Part I: The Models

  • Li-Xin Wang
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    In this paper we use fuzzy systems theory to convert the technical trading rules commonly used by stock practitioners into excess demand functions which are then used to drive the price dynamics. The technical trading rules are recorded in natural languages where fuzzy words and vague expressions abound. In Part I of this paper, we will show the details of how to transform the technical trading heuristics into nonlinear dynamic equations. First, we define fuzzy sets to represent the fuzzy terms in the technical trading rules; second, we translate each technical trading heuristic into a group of fuzzy IF-THEN rules; third, we combine the fuzzy IF-THEN rules in a group into a fuzzy system; and finally, the linear combination of these fuzzy systems is used as the excess demand function in the price dynamic equation. We transform a wide variety of technical trading rules into fuzzy systems, including moving average rules, support and resistance rules, trend line rules, big buyer, big seller and manipulator rules, band and stop rules, and volume and relative strength rules. Simulation results show that the price dynamics driven by these technical trading rules are complex and chaotic, and some common phenomena in real stock prices such as jumps, trending and self-fulfilling appear naturally.

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    File URL: http://arxiv.org/pdf/1401.1888
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    Paper provided by arXiv.org in its series Papers with number 1401.1888.

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    Date of creation: Jan 2014
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    Handle: RePEc:arx:papers:1401.1888
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    1. Andrew Lo & Harry Mamaysky & Jiang Wang, 1999. "Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation," Computing in Economics and Finance 1999 402, Society for Computational Economics.
    2. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    3. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. " Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-64, December.
    4. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. " Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    5. Allan Timmermann & Halbert White & Ryan Sullivan, 1998. "Data-Snooping, Technical Trading, Rule Performance and the Bootstrap," FMG Discussion Papers dp303, Financial Markets Group.
    6. 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.
    7. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. Gencay, Ramazan, 1998. "The predictability of security returns with simple technical trading rules," Journal of Empirical Finance, Elsevier, vol. 5(4), pages 347-359, October.
    9. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    10. 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.
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