迴歸分析與類神經網路此兩種方法皆是預測領域上的主要工具。本論文嘗試在線性迴歸模式及非線性迴歸模式的條件下，隨機產生不同特性的資料以完整探討資料特性對迴歸分析與類神經網路之預測效果的影響。這些特性包括常態分配、偏態分配、不等變異、Michaelis-Menten關係模式及指數迴歸模式。 再者，我們使用區域搜尋法(local search methods)中的演化策略法(evolution strategies，ES)作為類神經網路的學習(learning)方法以提高其預測功能。我們稱這種類型的類神經網路為ESNN。 模擬結果顯示，ESNN確實可以取代常用來與迴歸分析做比較的倒傳遞類神經網路(back-propagation neural network，BPNN)，成為類神經網路的新選擇。針對不同特性的資料，我們建議：如果原始的資料適合以常態線性迴歸模式配適，則使用者可考慮使用迴歸方法做預測。如果原始的資料經由圖形分析或由檢定方法得知違反誤差項為均等變異之假設時，若能找到合適的權數，可使用加權最小平方法，但若權數難以決定時，則使用ESNN做預測。如果資料呈現韋伯偏態分佈時，可考慮使用ESNN或韋伯迴歸方法。資料適合以非線性迴歸模式做配適時，則選擇以ESNN做預測。 關鍵詞：迴歸分析，類神經網路，區域搜尋法，演化策略法類神經網路，倒傳遞類神經網路 / Both regression analysis and artificial neural networks are the main techniques for prediction. In this research, we tried to randomly generate different types of data, so as to completely explore the effect of data characteristics on the predictive performance of regression analysis and artificial neural networks. The data characteristics include normal distribution, skew distribution, unequal variances, Michaelis-Menten relationship model and exponential regression model. In addition, we used the evolution strategies, which is one of the local search methods for training artificial neural networks, to further improve its predictive performance. We name this type of artificial neural networks ESNN. Simulation studies indicate that ESNN could indeed replace BPNN to be the new choice of artificial neural networks. For different types of data, we commend that users can use regression analysis for their prediction if the original data is fit for linear regression model. When the residuals of the data are unequal variances, users can use weighted least squares if the optimal weights could be found. Otherwise, users can use ESNN. If the data is fit for weibull distribution, users can use ESNN or weibull regression. If the data is fit for nonlinear regression model, users can choose ESNN for the prediction. Keywords: Regression Analysis, Artificial Neural Networks, Local Search Methods, Evolution Strategies Neural Network (ESNN), Back-propagation Neural Network (BPNN)

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.

面對市場未來趨勢的不確定性，投資者可以運用「投資組合保險」的概念，既能保障原本所投資的資產價值，又可以參與市場上漲時的獲利。本研究以類神經網路來研究證券市場的現象，一方面是已經有許多類神經網路在財務分析上的研究成果，另一方面是其具有學習以及預測的能力。 本研究首先探討投資組合保險策略，接著再比較投資組合保險策略在不同市況下的績效表現，隨後提出兩個階段的研究架構，經過設計與建置，以類神經網路模型進行對大盤未來漲跌型態的模擬預測，並利用預測的結果，輔助投資組合保險策略的決策，最後並將研究結果與大盤績效做綜合分析比較。 本研究的資料採取自台灣證券集中交易市場，期間為1991年1月3日至2002年12月31日，共3306個交易日，取大盤每日交易之歷史資料，經過處理後建立資料庫。類神經網路模型具有預測未來大盤漲跌區間的能力，在本研究所提出的漲跌區間劃分方式上，其預測正確率達到55%，預測的結果與實際漲跌完全相反的比例僅10%，其餘的35%為相鄰區間的預測誤差，其預測能力有助於投資組合保險策略的進行。 經過類神經網路模型輔助而進行的停損策略（SL），其年報酬率以及Sharpe Ratio，在大盤下跌的期間，兩個績效指標衡量結果皆為正值（21.125%＞0以及980.493＞0），充分發揮保險功能；而在大盤上漲的期間，兩個績效指標衡量結果皆優於大盤（46.544%＞17.137%以及393.808＞110.069）。 在年報酬率與Sharpe Ratio之間，本研究主張在探討投資組合保險時應著重風險的衡量，因此經過類神經網路模型輔助而進行的固定比例投資組合策略（CPPI），搭配槓桿乘數M值的調整，在大盤下跌的期間，其Sharpe Ratio依然可以維持正值，達到保險的效果，保護投資人的資產免於損失；而在大盤上漲的期間，其Sharpe Ratio更是高於大盤，可以享受資產價值提昇的獲利。 / Facing the uncertainty of the market trend, an investor can use the concept of “ Portfolio Insurance ” to protect the value of his portfolio in bear market and earn the benefit from bull market. There have been many researches about applying Neural Network in the financial analysis and Neural Network has the abilities to learn and forecast. This research evaluates the performances of the portfolio insurance strategies in different market trends. Then two-stage research structure has been designed and built. The first stage is forecasting the up-and-down trends of the equity market index by Neural network model. The second stage is using the forecasted results assisting the portfolio insurance decisions. Finally, the results of this research have been analyzed and compared with the benchmark. The Neural Network is able to forecast the future up-and-down trends. The accurate rate is 55%. During the bear market（2002）, the annual rate of return and Sharpe Ratio of the stop loss（SL） strategy which is assisted by NN are both positive（21.125%＞0 and 980.493＞0）. During the bull market（2001）, they both outperform the benchmark（46.544%＞17.137% and 393.808＞110.069）. The annual rate of return is more important than Sharpe Ratio because the risk measurement is an important factor in portfolio insurance strategy. Sharpe Ratios of the CPPI strategy which is assisted by NN outperform the benchmark in both above mentioned bear and bull market. In short, the SL and CPPI strategy assisted by NN not only protect the value of the portfolio from losing in bear market but also gain profit in bull market, so they are the ideal portfolio insurance strategies.

當市場上有訊息產生時，由於市場機制的限制或其他因素影響，例如投資人的心理，導致不同股票在傳導訊息時存在時間上的落差，因此產生反應訊息領先其他股票的指標股，在本研究中將利用兩種方法：矩陣自我迴歸及類神經網路檢測市場上是否存有指標股、其特性為何？及指標股是否具有穩定性。 　 實證結果發現規模較大及流動性較高的股票在市場呈現多頭行情時其訊息傳遞確實具有領先效果且領先時期達六至十二個營業日，而券商於報章雜誌上推薦之指標股並不具備領先反應訊息的能力。此外，在市場呈現空頭時期，所有股票反應訊息的速度幾乎一致。

This research employs five predicting variables to implementing the market timing strategy. These five variables are E/P1, E/P2, B/M, CP and GM. The investment performances of market timing under a variety of investment horizons are examined. There are four different forecasting horizons, which are one-month, three-month, six-month, and twelve-month investment horizons. Both the linear approach and artificial neural networks are employed to forecasting the market. The artificial neural network is employed with a view to capture the non-linearity property embedded in the market. The results are summarized as follows. (1) Both the linearity and nonlinear approaches are able to outperform the market. According to the results of Cumby-Modest test, they do have the market timing ability. (2) In the simple regression models, the performance of CP is relatively well compared to those of other variables. (3) The correct prediction rate increases as the investment horizon increases. (4) The performance of the expanding window approach is on average inferior to that of the moving window approach. (5) In the simulations of timing abilities over the period of May, 1991 to December, 1997. The multiple regression models has the best performance for the cases of one-month, three-month, and six-month investment horizons. On the other hand, BP(1) has the best performance for the case of one-year investment horizon. Contents Chapter 1 Introduction ……………………………………… 1 1.1 Background……………………………………………………………. 1 1.2 Motivations and objectives…………………………………………….3 1.3 Thesis organization ………………………………………………….. 4 Chapter 2 Literature Review…………………………………6 2.1 Previous studies on market timing……………………………………. 6 2.2 Predicting variables…………………………………………………… 8 2.3 Artificial Neural Networks……………………………………………10 2.4 Back Propagation Neural Networks…………………………………..11 2.5 Applications of ANNs to financial fields………………….………….12 Chapter 3 Data and Methodology……………………….….15 3.1 Data………………………………………………………………..….15 3.2 Linear approaches to implementing market timing strategy……….…18 3.3 ANNs to implementing market timing strategy…………..…………..23 Chapter 4 Results on Timing Performance……………..…26 4.1 Performance of linear approach………………………………………26 4.2 Performance of ANNs………………………………………………...38 4.3 Performance evaluation……………………………………………….39 Chapter 5 Summary…………………………………………54 5.1 Conclusions……………………………………………………….….54 5.2 Future works…………………………………………………………55 Appendix……………………………………………………..56 References……………………………………………………57 / This research employs five predicting variables to implementing the market timing strategy. These five variables are E/P1, E/P2, B/M, CP and GM. The investment performances of market timing under a variety of investment horizons are examined. There are four different forecasting horizons, which are one-month, three-month, six-month, and twelve-month investment horizons. Both the linear approach and artificial neural networks are employed to forecasting the market. The artificial neural network is employed with a view to capture the non-linearity property embedded in the market. The results are summarized as follows. (1) Both the linearity and nonlinear approaches are able to outperform the market. According to the results of Cumby-Modest test, they do have the market timing ability. (2) In the simple regression models, the performance of CP is relatively well compared to those of other variables. (3) The correct prediction rate increases as the investment horizon increases. (4) The performance of the expanding window approach is on average inferior to that of the moving window approach. (5) In the simulations of timing abilities over the period of May, 1991 to December, 1997. The multiple regression models has the best performance for the cases of one-month, three-month, and six-month investment horizons. On the other hand, BP(1) has the best performance for the case of one-year investment horizon.

國小教師供需問題是目前教育界中的一個重要問題，教師需求量的預測精確與否，將影響及教育政策的制定。本研究中，我們使用單變量 ARIMA 及類神經網路，以預測台灣地區 1996 到 1998 年之間的國小教師需求量。 研究結果顯示，在預測國小教師數列上，ARIMA 及類神經望陸均有很好的表現。類神經網路的可用範圍寬廣，適於各種複雜的情境，然而就本研究的主要探討對象--國小教師數列而言，以單變數的神經網路便已足夠。如果能選擇適當、具明顯特徵的資料，則網路將有更佳的預測效果。 由於類神經網路具有自我學習、自我調適、及平行處理等優點，因此在發展教師供需預測系統時，除了 ARIMA 之外，類神經網路為另一可行方法。 / The demand for and supply of teachers in elementary schools is an important problem in education administration. An accurate forecast of the number of teachers needs in elementary schools may heavily affect educational policy. In this thesis, we use the univariate time series analysis and Neural Networks to forecast the number of teacher in elementary schools in Taiwan Area during a period from 1996 to 1998. According to the result, both Box-Jenkins model and Neural Network perform well for prediction. Neural Network can be widely used in different circumstance, especially complicated situation. In this research, however, it is enough to predict number of teacher by the univariate neural network. In other word, if selecting suitable data variables, we could obtain better predictable effect by neural network. With the advantages of self-learning, self adaptation, and parallel processing, the Neural Network approach is a promising alternative approach to time series for developing a teacher demand and supply forecasting system.

在資訊來源日趨複雜化及多樣化之下，過多不必要的資訊反而造成決策上的困擾，因此資訊的篩選(Information Filtering)便成為設計資訊系統時所要考量的重要因素之一。資訊的有效篩選不僅使得決策的不確定性降低，同時讓決策人員能夠專注於對決策有重要影響的因素上，提高了決策的效率與品質。本研究即是以逆傳遞(Back Propagation)類神經網路模式(Artificial Neural Network Model)為基礎，設計一個能夠篩選出重要屬性的通用演算法；此演算法能夠幫助使用者去除一些對決策較無影響的屬性，讓使用者能夠減少資訊收集成本，並針對重要屬性做決策上的考量。同時在本研究中，我們還將此演算法應用在生產現場的屬性篩選上，幫助排程人員找出對於排程法則選取有重要影響的屬性；並藉此驗證篩選演算法的正確性及完整性。 / To screen the mformation effectively can improve the efficiency and quality of decision making dramatically. Since it does not only decrease the uncertainty of decision maldng, but also let decision makers can emphasize on the important factors which can significantly affect the result of decision. In this thesis we present an algorithm to find the important factors out based on the technique of back propagation neural network model. This algorithm can help users to remove some attributes which do not or seldom affect the result of decision, and let them can reduce the cost of data collection and emphasize on consideration of the remaining important attributes. And in this thesis, we also apply the algorithm to filter out the important production attributes of shop floor scheduling system which can significantly affect the selection of shop floor scheduling rules, and use the result of this experiment to verify the correctness and completeness of the algorithm.

隨著證券市場規模不斷擴大，投資人越來越難以選擇投資標的，電腦之超強計算能力，應可幫助投資人進行證券投資。但傳統之電腦處理方式難以適應迅息萬變之外在環境，若一模式能自我學習、自我調整，如同人一般學習，再輔以其快速的資料處理能力，應能幫助投資人進行投資。類神經網路(Neural Network)，被稱為「第六代電腦」，即具有自我學習調整能力。 　　本研究使用貝氏(Bayesian)類神經網路，其屬於非監督式類神經網路，具有學習時間短、理論健全之機率型(Probability)類神經網路。理論上，盈餘影響公司未來成長及股利，進而反應於其股價。而盈餘又是一公司各項決策之經營成果，經營決策將顯示於各項財務數字及比率。故我們以財務比率訓練其掌握該企業明年度盈餘成長或衰退之類神經網路，進而以該預測結果運用於擬證券投資以觀察其有用性。 　　實證研究結果顯示，若訓練樣本中包含大多偏差值(Outliner)，則將破壞網路之機率分配，使網路無法架構。去除偏差值後，再進行網路訓練，則有約百分之七十的預測未來盈餘走向正確率，若訓練樣本再去除灰色地帶(Gray Aera)之樣本，即盈餘處於不成長不衰退之間的樣本，正確率可再稍微提升。模擬投資結果顯示運用貝氏類神經網路於證券投資所獲得之超額報酬率，高於銀行業最高定期存款報酬率，顯示本研究模式應有可取之處。

隨著全球化與資訊科技之進步，大幅加快媒體傳播訊息之速度，使得與股票市場相關之新聞事件，無論在產量、產出頻率上，都較以往增加，進而對股票市場造成影響。現今投資者多已具備傳統的投資概念、觀察總體經濟之趨勢與指標、分析漲跌之圖表用以預測股票收盤價；除此之外，從大量新聞資料中，找出關鍵輔助投資之新聞事件更是需要培養的能力，而此正是投資者較為不熟悉的部分，故希望透過本文加以探討之。 　　本研究使用2009年自由時報電子報之財經新聞（共5767篇）為資料來源，以文件距離為基礎之kNN技術分群，並採用時間區間之概念，用以增進分群之時效性；而分群之結果，再透過類別詞庫分類為正向、持平及負向新聞事件，與股票市場之量化資料，包括成交量、收盤價及3日收盤價，一併輸入於倒傳遞類神經網路之預測模型。自台灣經濟新報中取得半導體類股之交易資訊，將其分成訓練及測試資料，各包含168個及83個交易日，經由網路之迭代學習過程建立預測模型，並與原預測模型進行比較。 　　由研究結果中，首先，類別詞庫可透過股票收盤價報酬率及篩選字詞出現頻率的方式建立，使投資者能透藉由分群與分類降低新聞文件的資訊量；其次，於倒傳遞類神經網路預測模型中加入分類後的新聞事件，依統計顯著性檢定，在顯著水準為95%及99%下，皆顯著改善隔日股票收盤價之預測方向正確性與準確率，換言之，於預測模型中加入新聞事件，有助於預測隔日收盤價。最後，本研究並指出一些未來研究方向。

隨著國內不少優秀的棒球選手進入美國職棒聯盟，而且運動彩券也於民國97年正式發行，除了創造專業運動評論的需求，也吸引了國人對於運動彩券投注的興趣，因此我們希望透過分析歷史資料來預測棒球賽事。 本論文中，我們從球隊得分的觀點切入，建立棒球賽事的預測模型，期望透過預測兩支球隊的得分，來推論賽事結果，並可當作投注運彩的策略。 我們的預測模型結合了類神經網路與迴歸分析的理論，首先透過類神經網路去預測球隊的打擊表現，接著利用迴歸分析的技術，並參考Pete Palmer提出的Batting Runs公式，為每支球隊建立專屬的得分公式，然後將預測的打擊表現套用得分公式，計算球隊的預測得分。最後根據預測結果來模擬投注棒球運動彩券，並分析報酬率。 實作時，我們採用美國棒球聯盟近三年之資料來測試我們的方法，實驗結果顯示，我們預測的結果能獲得不錯的報酬率。 / There are many outstanding Taiwanese baseball players who joined the MLB in the USA, and the sport lottery has been issued in 2008. These have not only generated the demand for professional commentaries on various sports but also attracted numerous interests in sport lottery playing. Hence, we hope to predict the future baseball game results through analyzing the historical data. In this thesis, we started from the scoring mechanism and developed a model to predict baseball games. We used the predicted results, together with the sports lottery playing regulations, to find the lottery winning strategies. We used artificial neural networks and regression analysis in our model. Through the neural networks we can predict the batting behaviors of each team. Then, we used the regression analysis and the batting runs formula, proposed by Pete Palmer, to establish the scoring formula for each team. Combining the batting behaviors and the scoring formula, we can predict the scores of the future baseball games. Finally, we used the predicted scores to estimate the winning rate of sports lottery on these baseball games. We used the materials in the past three years of MLB in USA to verify our method. The experimental results show that we can obtain good winning rate.