渾沌理論與個股走勢分析探討： 以中鋼為例

Abstract

古典理論所揭櫫的世界，是一個可以用線性模型做推論的世界，只要輸入適當的參數，就如同蘋果一定會掉到地上，未來也是可預測的，若有預測失真的現象，古典理論視為雜訊，置之不理；但是現實並非如此，線性系統不過是在實驗室所控制的環境底下所產生，所以非線性、不確定性系統充斥於這個世界，所以開始有許多研究及理論認為非線性系統比較貼近真實。近代最知名的非線性系統動力學即是渾沌理論，各種不同的學術均把渾沌理論應用在各自的學術中，打破了學術界間的藩籬。 金融市場上對價格趨勢的研究很多，其中渾沌理論也是近年來所討論較多的理論。渾沌系統有幾個必要條件：系統是開放的、非線性的、以及非平衡的，而股票市場具有上述的特質；雖然目前對股票市場的渾沌現象還沒有定論，但是或許可以指出：股票市場可被視為渾沌系統，而西元1938年由艾略特 (Nalph Nelson Eilliott) 所提出的波浪理論 (The Wave Principle) 就是這個發現。波浪理論是將金融市場上的價格趨勢型態，歸納出幾個不斷覆出現的型態，為研究價格趨勢型態種類最完整的研究。 渾沌理論最大的危機在於本身無強大的數學工具為基礎，如此一來，所面臨的瓶頸便是一個可預期且必然的結果；本研究旨在探討個股時間序列之渾沌現象，並使用統計理論中時間序列檢定方式，嘗試建立一種嚴謹驗證渾沌現象的方式。 本研究最後驗證，中鋼股價之時間序列為低維度之渾沌系統。

Classical theories tell, the world can be explained by a linear model, with certain variables, the future is predictable, as the apple must fall to the ground; If the prediction is not correct, there must be some minor noise issues. The real world tells the different story. Uncertainty and nonlinear system are everywhere in the world, linear systems happened under control environments. Nonlinear systems become the real world. Recently, the most famous nonlinear dynamics system theory is Chaos, almost every academics theory is trying to use Chaos System into its domain, breaking the wall of different academics. There’re many studies about stock price trend analysis. Recently, Chaos Theory is often discussed. Some characteristics are necessary to define a chaos system: open, non-linear and un-balanced. These characteristics can be found on the stock market. Although conclusion has not been given yet, however, we might be able to point out that, the stock market can be treated as a chaos system, and the Wave Principle, which announced by Nalph Nelson Eilliott in 1938, is the finding. The Wave Principle concludes several price trend types of the financial market, which repeated again and again on the market, it is the most complete price trend types study. The most difficult part of Chaos System is, no well-defined system to determinate a system is a Chaos System or not, so bottlenecks happened. This study tries to use a systematic method, which might be useful to identify the Chaos System, and discusses the chaos phenomenon of the time series of a stock price trend. In the end, this study proves that, the stock price time series of China Steel Corp. is a low dimension Chaos System