臺灣博碩士論文加值系統

財務時間序列預測一直是財務決策之重要議題，但由於財務時間序列資料具有高頻率、雜訊、非定態與混沌等性質，使得其在時間序列預測領域中，向來被認為是一極具挑戰性的應用領域。支援向量迴歸（Support vector regression, SVR）是一個以統計學習理論（Statistical learning theory）為基礎的預測方法，由於具有全域最佳解（Global optimum）及考慮結構風險（Structural risk）的特性，SVR已成功的應用於時間序列預測的議題；除此之外，類神經網路（Artificial neural network, ANN）由於擁有非線性與學習動態系統的特性，可以自動找出資料中所隱含的模式或特徵，使得ANN在建構變數間為非線性資料型態的預測問題中也有優越的表現。在使用SVR與ANN建立預測模式時，資料中的雜訊會影響建構預測模式的準確率，由於財務時間序列資料最重要的特徵就是包含許多的雜訊，因此如何偵測及去除資料中的雜訊，降低其對SVR與ANN預測模式之影響，就成為重要的研究議題。
獨立成份分析（Independent components analysis, ICA）是一個新穎的訊號處理技術，其主要目的是在沒有任何有關訊號混合的事前資訊下，從觀察到的混合訊號（Mixing signals）中找出原始的來源訊號（Source signals）。由於時間序列的雜訊往往無法由觀察到的混合訊號中獲得相關的資訊，因此本研究先利用ICA具有將混合訊號分離出個別獨立來源訊號之能力，從預測變數中估計出獨立成份，並去除代表雜訊的獨立成份及保留主要的獨立成份作為預測變數後，再使用SVR與ANN以濾除雜訊後之預測變數建構預測模式，整體而言，本研究提出兩種預測模式，一為結合ICA與SVR之預測模型，另一則為結合ICA與ANN之預測模型；期望可以讓SVR與ANN在建構模式時不受雜訊影響，進而提升預測結果的準確度。
為驗證所提方法之有效性，本研究將以日經225（Nikkei 225）現貨開盤價格及台灣加權股價指數（Taiwan stock exchange capitalization weighted stock index）收盤價格進行實證研究，並與單純使用預測工具模式、隨機漫步（Random walk）模式及其他常用的去除雜訊方法-簡單移動平均（Simple moving average）及小波框架（Wavelet frame）之預測結果作比較。實證結果顯示，整體而言，所提之方法不論在預測誤差或是趨勢預測準確度的表現上均較單純使用預測工具、隨機漫步、簡單移動平均及小波框架為佳。

As financial time series are inherently noisy, non-stationary and deterministically chaotic, it is one of the most challenging applications of modern time series forecasting. Due to the advantages of building nonparametric and nonlinear models, support vector regression (SVR) and artificial neural network (ANN) have been successfully applied in time series prediction, especially in the financial time series forecasting. In the modelling of financial time series using SVR and ANN, one of the key problems is the inherent high noise. Therefore, detecting and removing the noise are important but difficult tasks when building an SVR and ANN forecasting models. In this research, two forecasting models using independent component analysis (ICA), SVR and ANN are proposed for financial time series forecasting. ICA is a novel statistical signal processing technique that was originally proposed to find the latent source signals from observed mixture signal without knowing any prior knowledge of the mixing mechanism. The proposed approaches firstly use ICA to the forecasting variables for generating the independent components (ICs). After identifying and removing the ICs containing noise, the rest of the ICs are then used to reconstruct the forecasting variables which contain less noise. The SVR and Back-propagation neural network (BPN) are then respectively applied to use the filtered (or denoised) forecasting variables to build the forecasting models. In order to evaluate the performance of the proposed approaches, the Nikkei 225 opening cash price index and TAIEX are used as the illustrative examples. The experimental results show that the proposed models outperforms the SVR and BPN model with non-filtered forecasting variables, random walk model, simple moving average model and wavelet frame model in forecasting performance.

中文摘要…………………………………………………………………….. Ⅰ
英文摘要…………………………………………………………………….. Ⅲ
誌謝………………………………………………………………………….. Ⅴ
目錄………………………………………………………………………….. Ⅵ
圖次………………………………………………………………………….. Ⅸ
表次………………………………………………………………………….. ⅩⅠ

第一章 緒論………………………………………………………………... 1
第一節 研究背景…………………………………………………………... 1
第二節 研究目的…………………………………………………………... 3
第三節 研究架構…………………………………………………………... 4
第二章 文獻探討…………………………………………………………... 5
第一節 財務時間序列預測………………………………………………... 5
第二節 類神經網路………………………………………………………... 7
第三節 支援向量迴歸……………………………………………………... 10
第四節 獨立成份分析……………………………………………………... 13
第三章 研究方法…………………………………………………………... 17
第一節 倒傳遞類神經網路………………………………………………... 17
3.1.1 類神經網路之架構………………………………………………... 17
3.1.2 倒傳遞類神經網路之架構………………………………………... 18
3.1.3 倒傳遞類神經網路之學習演算法………………………………... 21
第二節 支援向量迴歸……………………………………………………... 23
3.2.1 支援向量迴歸之架構……………………………………………... 23
3.2.2 支援向量迴歸之最適化問題……………………………………... 25
第三節 獨立成份分析……………………………………………………... 30
3.3.1 獨立成份分析之模型……………………………………………... 31
3.3.2 非高斯特性即為獨立性…………………………………………... 34
3.3.3 獨立性量測………………………………………………………... 35
第四節 結合ICA與SVR及BPN之方法……………………………………... 39
3.4.1 測試接受法（TnA）………………………………………………... 41
3.4.2 獨立成份選擇……………………………………………………... 44
第四章 實證結果分析……………………………………………………... 47
第一節 實證資料…………………………………………………………... 47
4.1.1 日經225開盤資料………………………………………………... 47
4.1.2 台灣加權股價指數收盤資料……………………………………... 50
第二節 評估準則..………………………………………………………... 53
第三節 結合ICA與BPN之預測結果………………………………………... 54
4.3.1 日經225開盤資料…………………………………………………... 54
4.3.2 台灣加權股價指數收盤資料……………………………………... 59
第四節 結合ICA與SVR模式之預測結果…………………………………... 68
4.4.1日經225開盤資料…………………………………………………... 68
4.4.2台灣加權股價指數收盤資料………………………………………... 69
第五節 ICA與其他去除雜訊方法的比較………………………………... 71
第六節 選擇不同個數之獨立成份代表雜訊之影響……………………... 74
第五章 結論與建議………………………………………………………... 76
第一節 結論………………………………………………………………... 76
第二節 研究貢獻…………………………………………………………... 77
第三節 後續研究建議……………………………………………………... 78
參考文獻……………………………………………………………………... 80
附錄A：FastICA演算法…………………………………………………... 96
附錄B：各預測模型在不同參數組合下的訓練及測試結果……………... 101
B.1 日經225開盤資料-BPN……………………………………………... 101
B.2 台灣加權股票指數收盤資料-BPN…………………………………... 103
B.3 日經225開盤資料-SVR……………………………………………... 106
B.4 台灣加權股票指數收盤資料-SVR…………………………………... 108
附錄C：結合其他去雜訊方法之SVR預測模型在不同參數組合
下的訓練及測試結果……………………………………………...110
C.1 日經225開盤資料……………………………………………………... 110
C.2台灣加權股票指數收盤資料…………………………………………... 112
附錄D：不同獨立成份還原之預測模型在不同參數組合
下的訓練及測試結果……………………………………………... 115
附錄E：結合其他去雜訊方法之BPN預測模型在不同參數組合
下的訓練及測試結果……………………………………………... 117
E.1 日經225開盤資料……………………………………………………... 117
E.2 台灣加權股票指數收盤資料………………………………………... 120
附錄F：交易策略…………………………………………………………... 123
F.1 日經225開盤資料……………………………………………………... 123
F.2台灣加權股票指數收盤資料…………………………………………... 125

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