ARIMA與適應性SVM之混合模型於股價指數預測之研究

A Hybrid ARIMA and Adaptive SVM Model in Forecasting Stock Market Index

股價指數是一種高度不穩定、複雜且難以預測的時間序列資料，而時間序列的預測，傳統以統計技術為主，近來則以類神經網路技術較受重視。一般而言，自我迴歸整合移動平均 (auto regression integrated moving average, ARIMA) 及支援向量機 ( support vector machine, SVM) 分別對於線性及非線性資料之預測效能頗佳，因此資料首 先經由ARIMA模型的建立，得出一個線性預測值，而由於傳統的SVM並沒有考量時間因素的影響，因此本研究調整原本固定之ε係數建構一隨時間遞減的動態形式之ε-DSVM，並以此預測由之前ARIMA模型產生之殘差項的估計值，藉由此兩模型之 結合即可得到預測值，而後以實例驗詮此調整後之混合模型之績效。本研究假設股價之走勢為不受非市場因素影響的隨機過程，並以美國紐約證交所道瓊工業指數過去一年的走勢為實驗資料樣本，樣本資料切割為互斥的五個均等份子集以進行交叉驗證，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，故混合模型可大幅改善預測效能，並顯著地減少預測誤差。

The stock market index is unstable, complicated, and unpredictable. In attempting to predict time series data, statistical methods are the major research stream in tradition, but recent years have seen increased attention to the techniques of neural networks. It has been recognized that the auto regression integrated moving average (ARIMA) and the support vector machine (SVM) perform fairly well in predicting linear and nonlinear time series data, respectively. However, the factor of time is often overlooked. In this paper, an adaptive SVM is proposed by modifying the regularized risk function in which the more recent ε-insensitive errors would be penalized more heavily than the older e-insensitive errors. An experiment is validated to demonstrate the effectiveness of the hybrid adaptive SVM and ARIMA model. The Dow Jones industrial indexes for the past one year are used for the experiment where the data sample is divided into five exclusive partitions to proceed a five-fold cross validation. Mean square error (MSE), mean absolute error (MAE), and directional symmetry (DS) are used to examine the performance of the proposed model. The results show that the hybrid model performs better than ARIMA, SVM, and ARIMA + SVM models, and it is able to significantly improve the prediction performance and substantially decrease the prediction error.