股市指數是一個高度不穩定、複雜且難以預測的時間序列資料，時間序列的預測，傳統上可用統計模型，近來則常用類神經網路技術。自我迴歸整合移動平均(auto regression integrated moving average, ARIMA)模型在線性資料預測有極佳之效能，而支援向量機(support vector machine, SVM)模型則在非線性資料預測有極佳之效能，然而傳統的支援向量機並沒有將時間的影響考量進去，故本研究將原本固定的ε係數動態調整為隨時間遞減的形式，並以實例驗證此調整後的支援向量機與ARIMA之混合模型的使用可得到較兩最佳模型之更優越的效能。因此本研究假設股價之走勢為不受非市場因素影響，亦不受人為操縱影響的隨機過程，並以道瓊工業指數過去一年的走勢為實驗資料樣本，首先以ARIMA模型預測道瓊工業指數，得到一組序列預測值與殘差項序列，將此組殘差序列以下降ε支援向量機(ε-descending support vector machine,ε-DSVM)模型訓練，得到殘差項預測值，將ARIMA模型的預測值與殘差項序列的預測值加總即為混合模型之預測值。模型訓練完成後，將樣本資料均等份切割為互斥的五個子集，並進行交叉驗證，計算各個子集的均方差(mean square error, MSE)、絕對誤差(mean absolute error, MAE)與方向對稱性(directional symmetry, DS)等三項指標衡量它的效能。實驗結果發現，混合模型的預測效能及精確度，均較ARIMA、SVM與ARIMA+SVM三個簡單模型為佳，故混合模型可大幅度地改善預測效能，並大量減少預測誤差。

The stock market index is unstable, complicated, and unpredictable. Statistical models are used for predicting the time series in tradition. Recently, neural networks have been successfully used for modeling financial time series data. The auto regression integrated moving average (ARIMA) model has good performance in predicting linear data, and the support vector machine (SVM) has good performance in predicting nonlinear data. The adaptive SVM are obtained by a simple modification of the regularized risk function in support vector machines, whereby the recent ε-insensitive errors are penalized more heavily than the distant ε-insensitive errors. An experiment is validated to show that the hybrid adaptive SVM and ARIMA model can result in more superior performance than the two individual models. The data sample is composed of the past one year of Dow Jones industrial index. The ARIMA model is used to predict Dow Jones Industrial Index in the beginning, and then two series of estimates and residuals are obtained. Using the ε-descending support vector machine (ε-DSVM) model to train the residual series would get a series of residual estimates. At the end of training process, the data sample is divided into five exclusive partitions to proceed the five-fold cross validation. Mean square error (MSE), mean absolute error (MAE), and directional symmetry (DS) are used to measure the performance of the proposed model. The result of experiment shows that the prediction effectiveness and accuracy of the hybrid model are better than ARIMA, SVM, and ARIMA+SVM models. The hybrid model could greatly improve the prediction performance and effectively decreases the prediction error.

中文部分
詹琇伃，「結合ARIMA模式與倒傳遞網路以降低預測誤差」，國立成功大學工業與資訊管理研究所碩士論文，民93。
王琡閔，「股價預測之統計模型」，國立中央大學統計研究所碩士論文，民90。

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