近年來，支援迴歸向量機已成功地被用來解決證券市場預測的問題。然而，支援迴歸向量機需要手動的調整核心函數的超參數。因此有學者提出多核心學習法來解決這類的問題，其中核心矩陣的權重向量與拉格朗日乘數常使用半正定規劃法來同時解得。但這類的演算法需要很大量的時間與空間，因此本論文提出一種結合最小序列優化法與梯度投影法的兩階段多核心學習演算法。
根據本演算法，使用者可以合併多個不同的超參數而使整個系統預測效果得到改善並且不需事先指定超參數的設置，更避免了過去需反覆實驗才可得到適合的超參數。本論文使用台灣加權指數加以實證，實驗結果顯示本方法效果優於其它的方法。

Support vector regression has been applied to stock market forecasting problems. However, it is usually needed to tune manually the hyperparameters of the kernel functions. Multiple-kernel learning was developed to deal with this problem, by which the kernel matrix weights and Lagrange multipliers can be simultaneously derived through semidefinite programming. However, the amount of time and space required is very demanding. We develop a two-stage multiple-kernel learning algorithm by incorporating sequential minimal optimization and the gradient projection method.
By this algorithm, advantages from different hyperparameter settings can be combined and overall system performance can be improved. Besides, the user need not specify the hyperparameter settings in advance, and trial-and-error for determining appropriate hyperparameter settings can then be avoided. Experimental results, obtained by running on datasets taken from Taiwan Capitalization Weighted Stock Index, show that our method performs better than other methods.

摘要 i
Abstract ii
目錄 iii
圖目錄 iv
表目錄 v
第一章 導論 1
1.1 研究動機 1
1.2 研究目的 4
1.3 論文架構 5
第二章 基礎理論 7
2.1 支援向量機器 7
2.1.1 線性分割 7
2.1.2 硬性邊界支援向量機 9
2.1.3 軟性邊界支援向量機 13
2.1.4 以核心運算為基礎的支援向量機 17
2.2 支援迴歸向量機 24
第三章 研究方法 27
3.1 多核心支援迴歸向量機 27
3.2 兩階段多核心學習 29
第四章 實驗結果 33
4.1 實驗一SKSVR與MKSVR比較 33
4.2 實驗二ARIMA、SKSVR與MKSVR比較 37
4.3 實驗三FNN、SKSVR與MKSVR比較 42
第五章 結論與未來研究方向 46
5.1 結論 46
5.2 未來研究方向 46
參考文獻 47

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