時間序列的預測是困難的，尤其是證券市場指數的波動有著人為、經濟、政治、技術面和產業面等因素的影響，所以股價走勢的預測是更為不易的。現行預測的機制以類神經網路效能較佳，他們是非線性可調適性的模式，不須預先指定特別的型式就有能力去估計複雜的關係。自我組織特徵映射圖(Self-Organizing Map, SOM)是一個非監督式的類神經經網路，自我組織特徵映射圖能夠將高維度的資料藉由映射的方式對映至二維或一維的座標空間上，以利資料分群之進行。GM(1,1)是一種灰預測的基本模式，能在資訊不完整及不確定下具有系統預測的能力。
本學位論文提出一系列整合的時間序列預測機制，除了灰色自我組織特徵映射圖(Grey SOM based on GRG, GSOMGRG)，灰色傅立葉自我組織特徵映射圖(Grey Fourier SOM based on GRG, GFSOMGRG)外，另建立二階段灰色自我組織特徵映射圖模型(Two-stage GSOMGRG) 以及二階段灰色傅立葉自我組織特徵映射圖模型(Two-stage GFSOMGRG)，分別探討各模型在時間序列資料中估計和預測績效的表現。它們將傳統自我組織特徵映射圖與灰色理論的灰色關聯度(Grey Relational Grade, GRG)結合成一種新的聚類機制---灰關聯自我組織特徵映射圖 (SOM based on GRG, SOMGRG)，把一段時間序列資料視為一個幾何圖像，使用SOMGRG將圖像聚類，加上時間序列資料的前後處理機制，使得預測值的精確度更為提昇。此預測機制首先將時間序列進行GM(1,1)預測，再將其差分化的資料視為圖像，以灰關聯在自我組織特徵映射圖架構上進行圖像的聚類，之後將同類別資料的預測值進行修正，以得到更佳的預測值。在時間序列進行GM(1,1)預測過程中，GFSOMGRG增加了傅立葉殘差修正以增加GM(1,1)預測值準確度。在SOMGRG將圖像聚類時，two-stage 的機制進行二次聚類，以增進SOMGRG聚類的精確度。實驗數據中顯示Two-stage GFSOMGRG 比起其它模型預測能力更佳，進而能幫助投資者預測未來股票價格指數和掌握獲利的機會。

Time series prediction is a difficult task. The prediction of stock price trends is particularly difficult because the volatility of the stock market index is affected by human, economic, political, technical and industrial factors. Among the currently used prediction mechanisms, neural networks show the best performance. Neural networks are nonlinear adaptive models and have the ability to approximate complex relations which may not have a prespecified form. A self-organizing map (SOM) is an unsupervised neural network that uses the similarity of high-dimensional data in a two-dimensional or one-dimensional coordinate space to facilitate data classification. GM(1,1) is a basic model for grey prediction and is capable of providing system predictions under the constraints of uncertainty and imperfect information.
This paper presents a series of integrated time series prediction mechanisms. In addition to Grey SOM based on GRG (GSOMGRG) and Grey Fourier SOM based on GRG (GFSOMGRG), we explain the concepts of Two-stage GSOMGRG and Two-stage GFSOMGRG, which respectively predict and estimate the performance of models of time series data. The traditional SOM and Grey Relational Grade (GRG) of grey theory are combined into a new clustering mechanism, SOMGRG. A period of time series data is regarded as a pattern, and patterns are clustered with SOMGRG, together with the pre- and post-processing mechanisms of time series data, so that the accuracy of the predicted values is further enhanced. This prediction mechanism first uses GM(1,1) to predict the time series, and then the differencing data is regarded as forming patterns. The patterns are then clustered with GRG into a SOM structure. Then, the predicted values of the same type of data are modified to obtain better values. In the GM(1,1) predicting process, GFSOMGRG uses Fourier residual correction to increase the GM (1,1) prediction accuracy. For developing SOMGRG clustering patterns, a two-stage mechanism performs clustering twice in order to improve the accuracy of SOMGRG clustering. The experimental results show that Two-stage GFSOMGRG has better forecasting ability compared to other models and can help investors predict future stock price indices and grasp profit-making opportunities.

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