费波尼西数列之混沌现象的研究

　　2008.10.08　　来源：国立台湾大学.作者：周湘钧

　　艾略特藉由费波尼西数列的数理基础，以其中的“自然法则”来解释股价的波动趋势，发展出有名的艾略特波浪理论，足以解释1940年年代中期之前，他所能知晓的一切市场行为，并证实了它适用于研判道琼工业指数的走势发展。

　　混沌理论则是在最近这几年来震撼科学界，将复杂的科学搬上研究之路，企图找出“无序”与“秩序”之间的相关性的一种概念。

　　本篇论文除了针对费波尼西数列是否具有混沌理论所产生之现象，来做一番比较探讨之外，并且利用艾略特波浪理论来检测台湾股票市场是否具有费波尼西数列之特性。

　　得到以下的结论：

　　1、费波尼西数列具有混沌理论之现象，包括反馈系统，叠代作用，临界点，碎形，自我相似性，并且对于起始值具有强烈之敏感性，因此数列本身即为一混沌现象。

　　2、两理论的起源皆从自然界的现象之中观察而得。经由叠代过程，费波尼西数列发现0.618的黄金比例，而混沌理论的蛾成长模型，在出生率等于第3倍之前，族群数目始终稳定的停止在0.66的地方

　　3、国内大部分之股价走势，契合于艾略特波浪理论之原则，并且在股价趋势之脉动上，也接近费波尼西数列。由此即可得知，股价之走势具有类似性，且可从历史资料中找出相关性。只要解出费波尼西数列之神奇奥秘，则股价是可以预测的，并非全然的随机性。模型皆认为事物由本身之中，不断的相似，相似的过程持续的重覆着。

Research on Phenomenon of Chaos Theory in Fibonacci Sequence of Numbers -its Application in the Stock Market By using "nature principle" of the mathematical basis of "Fibonacci Sequence of Numbers," Elliott explained the fluctuating trends in stock prices by the development of a well-known "Elliott Wave Principle." This principle could explain all Market behaviors by the mid-1940s and has been proven that it could be applied to the research of Dow-Jones Industrial Index. The Chaos Theory that shocked the science field these years has turned complicated science into Empirical research with a view to finding the interaction between disorder and Order. Besides comparatively studying the Fibonacci Sequence of Number s phenomenon that is included in the Chaos Theory. The thesis also uses "Elliott Wave Curve" to examine whether Taiwan Stock market exists the Characteristics of Fibonacci Sequence of Numbers Thesis Conclusion: 1. The Fibonacci Sequence of Numbers exists phenomenon from Chaos Theory including Feedback, Iteration, Critical point, Fractal Structure, Self-similarity and intense sensitivity over start Value. The Fibonacci Sequence of Number itself, therefore, is one of phenomenon of Chaos Theory. 2. The origins of the Fibonacci Sequence of Numbers and Chaos Theory all attributed to empirical observance from the natural phenomena. By the process of iteration, the Fibonacci Sequence of Numbers finds out 0.618 golden Ratio, and the "Moth Growth Model" out of the Chaos Theory finds out the number of groups always stands at 0.66 before Its triple birth Rates. 3. Most fluctuations of Stock price in Taiwan follow the principles of Elliott Wave Curve theory moreover can be prove from Fibonacci Sequence of Numbers. This identifies that there is a similar trend in Stock price and Its interrelation also can be found from Information before. The Stock price, therefore, turns out not to be an over all random walk, but can be predicted of only to explain the mysteries of Fibonacci Sequence of Numbers. By proceeding Model research, it is proved that the objects will continuously resemble and repeat each other.

　　作者：周湘钧（JOU, SHIANG-JIUN）国立台湾大学.商学研究所