透過您的圖書館登入
IP:3.14.131.180
  • 學位論文

碎形維度與疊代函數系統之間的關係及其在股價預測上的應用

Relations Between Fractal Dimensions and Iterated Function Systems and Their Applications in Stock Market Prediction

指導教授 : 鄭志豪

摘要


我們會先介紹一些碎形幾何中的一些基礎定義,像是豪斯多夫距離、豪斯多夫維度、疊代函數系統及吸引子,並研究一些碎形理論的基礎結果,如:壓縮映射原理、拼貼定理、箱子計數定理、莫蘭定理,我們會用二維數據建造疊代函數系統,並證明疊代函數系統的係數及碎形維度之間的關係,最後藉由以上結果來進行股價預測。

並列摘要


We introduce some basic notions in fractal geometry such as Hausdorff distance, Hausdorff dimension, iterated function system (IFS) and attractor. Some fundamental results such as the contraction mapping principle, the collage theorem, the boxing counting theorem and the Moran theorem are studied. We construct IFS from some given data sets, and show that the coefficients of the IFS are related to the dimensions of the attractor of the IFS. These results are applied to stock market prediction.

參考文獻


[1] 胡家信(2013)。《分形分析引論》。北京:科學出版社。
[2] Micheal F. Barnsley, Fractals Everywhere (third ed), Dover Publication, New
York, (1993).
[3] Edgar. Gerald A, Measure, Topology, and Fractal Geometry, New York,
(2007).

延伸閱讀