在許多的研究和應用之中都需要預測的技巧。本論文中, 我們建構了一個 新的神經網路模式--動態徑向基底函數 (dynamical radial basis function) 網路 (DRBF網路) , 並且用這種模式的神經網路作為「函數近 似子」(function approximator) 去處理預測上的問題。另外我們也設計 幾種不同的學習演算法以測試DRBF網路的功能。 / The forecasting technique is important for many researches and applications. In this paper, we shall construct a new model of neural networks -- the dynamical radial basis function (DRBF) networks and use the DRBF networks as "function approximators" to solve some forecasting problems. Different learning algorithms are used to test the capability of DRBF networks.

本研究考慮重要且對台股大盤指數走勢有連動影響的因素，主要納入對台股有領頭作用的美國三大股市，那斯達克(NASDAQ)指數、道瓊工業(Dow Jones)指數、標準普爾500(S&P500)指數;其他對台股緊密連動效果的國際股票市場，香港恆生指數、上海證券綜合指數、深圳證券綜合指數、日經225指數;以及納入左右國際經濟表現的國際原油價格走勢，美國西德州原油、中東杜拜原油和歐洲北海布蘭特原油;在宏觀經濟因素方面則考量失業率、消費者物價指數、匯率、無風險利率、美國製造業重要指標的存貨/銷貨比率、影響貨幣數量甚鉅的M1B;在技術分析方面則納入多種重要的指標，心理線 (PSY) 指標、相對強弱(RSI) 指標、威廉(WMS%R) 指標、未成熟隨機(RSV) 指標、K-D隨機指標、移動平均線(MA)、乖離率(BIAS)、包寧傑%b和包寧傑帶狀寬度(BandWidth%);所有考量因素共計35項，因為納入重要因子比較多，所以完備性較高。 本研究先採用的贏者全拿(Winner-Take-All) 競爭學習策略的自組織映射網路(Self-Organizing Feature Maps, SOM)，藉由將相似資料歸屬到已身的神經元萃取出關聯分類且以計算距離來衡量神經元的離散特徵，對於探索大量且高維度的非線性複雜特徵俱有優良的因素相依性投射效果，將有利於提高預測模式精準度。在線性擬合部分則結合倒傳遞(Back-Propagation, BP)、Elman反饋式和徑向基底函數類網路(Radial-Basis-Function Network, RBF)模式為指數預測輸出，並對台股加權指數隔日收盤指數進行預測和評量。而在傳統的Elman反饋式網路只在隱藏層存在反饋機制，本研究則在輸入層和隱藏層皆建立反饋機制，將儲存在輸入層和隱藏層的過去時間資訊回饋給網路未來參考。在徑向基底函數網路方面，一般選取中心聚類點採用隨機選取方式，若能有效降低中心點個數，可降低網路複雜度，本研究導入垂直最小平方法以求取誤差最小的方式強化非監督式學習選取中心點的能力，以達到網路快速收斂，提昇網路學習品質。 研究資料為台股指數交易收盤價，日期自2001/1/2，至2011/10/31共2676筆資料。訓練資料自2001/1/2至2009/12/31，共2223筆;實證測試資料自2010/1/4至2011/10/31，計453個日數。主要評估指標採用平均相對誤差(AMRE)和平均絕對誤差 (AAE)。在考慮因子較多的狀況下，實證結果顯示，在先透過SOM進行因子聚類分析之後，預測因子被分成四個組別，分別再透過BP、Elman recurrent和RBF方法進行線性擬合，平均表現方面，以RBF模式下的四個群組因子表現最佳，其中RBF模式之下的群組4，其AMRE可達到0.63%，最差的AMRE則是群組1，約為1.05%;而Elman recurrent模式下的四組群組因子之ARME則介於1.01%和1.47%之間;其中預測效果表現最差則是BP模式的預測結果。顯示RBF具有絕佳的股價預測能力。最後，在未來研究建議可以運用本文獻所探討之其他數種類神經網路模式進行股價預測。 / In this study, we considering the impact factors for TWSE index tendency, mainly aimed at the three major American stock markets, NASDAQ index, Dow Jones index, S&P 500, which leading the Taiwan stock market trend; the other international stock markets, such as the Hong Kong Hang-Seng Index, Shanghai Stock Exchange Composite Index, Shenzhen Stock Exchange Composite Index, NIKKEI 225 index, which have close relationship with Taiwan stock market; we also adopt the international oil price trend, such as the West Texas Intermediate Crude Oil in American, the Dubai crude oil in Middle Eastern, North Sea Brent crude oil in European, which affects international economic performance widely; On the side of macroeconomic factors, we considering the Unemployed rate, Consumer Price Index, exchange rate, riskless rate, the Inventory to Sales ratio which it is important index of American manufacturing industry, and the M1b factor which did greatly affect to currency amounts; In the part of Technical Analysis index, we adopt several important indices, such as the Psychology Line Index (PSY), Relative Strength Index (RSI), the Wechsler Memory Scale—Revised Index (WMS%R), Row Stochastic Value Index (RSV), K-D Stochastics Index, Moving Average Line (MA), BIAS, Bollinger %b (%b), Bollinger Band Width (Band Width%);All factors total of 35 which we have considered the important factor is numerous, so the integrity is high. In this study, at first we adopt the Self-Organizing Feature Maps Network which based on the Winner-Take-All competition learning strategy, Similar information by the attribution to the body of the neuron has been extracted related categories and to calculate the distance to measure the discrete characteristics of neurons, it has excellent projection effect by exploring large and complex high-dimensional non-linear characteristics for all the dependency factors , would help to improve the accuracy of prediction models, would be able to help to improve the accuracy of prediction models. The part of the curve fitting combine with the back-propagation (Back-Propagation, BP), Elman recurrent model and radial basis function network (Radial-Basis-Function Network, RBF) model for the index prediction outputs, forecast and assessment the next close price of Taiwan stocks weighted index. In the traditional Elman recurrent network exists only one feedback mechanism in the hidden layer, in this study in the input and hidden layer feedback mechanisms are established, the previous information will be stored in the input and hidden layer and will be back to the network for future reference. In the radial basis function network, the general method is to selecting cluster center points by random selection, if we have the effectively way to reduce the number of the center points, which can reduces network complexity, in this study introduce the Orthogonal Least Squares method in order to obtain the smallest way to strengthen unsupervised learning center points selecting ability, in order to achieve convergence of the network fast, and improve network learning quality. Research data for the Trading close price of Taiwan Stock Index, the date since January 2, 2001 until September 30, 2011, total data number of 2656. since January 2, 2001 to December 31, 2009 a total number of 2223 trading close price as training data; empirical testing data, from January 4, 2010 to September 30, 2011, a total number of 433. The primary evaluation criteria adopt the Average Mean Relative Error (AMRE) and the Average Absolute Error (AAE). In the condition for consider more factors, the empirical results show that, by first through SOM for factor clustering analysis, the prediction factors were divided into four categories and then through BP, Elman recurrent and RBF methods for curve fitting, at the average performance , the four group factors of the RBF models get the best performance, the group 4 of the RBF model, the AMRE can reach 0.63%, the worst AMRE is group 1, about 1.05%; and the four groups of Elman recurrent model of ARME is between 1.01% and 1.47%; the worst prediction model is BP method. RBF has shown excellent predictive ability for stocks index. Finally, the proposal can be used in future studies of the literatures that we have explore several other methods of neural network model for stock trend forecasting.