股價預測是一個成熟的研究領域，統計學或機器學習等方法在這個領域被廣泛應用。然而，金融數據中的自然噪音對人類和計算機都構成挑戰。傅立葉變換在頻域去噪方面效果顯著，但發散問題仍然存在挑戰。為了應對這種發散，先前的方法提出使用隨機遊走來構造填充數據，從而孤立發散。然而，隨機遊走生成的填充數據引入了噪音，阻礙了更一致填充數據的推導，並增加了預測誤差。在這項研究中，我們介紹了一種基於 stationary bootstrap 填充和快速傅立葉變換 (SB-FTD) 的去噪技術。這種方法消除了頻域中的噪音，並提供了一種更一致的數據填充方法。這種方法改進了隨機遊走填充方法，並允許在不受噪音影響的環境中去噪原始序列的頻域特徵。我們的實證結果表明，所提出的去噪方法在預測能力和解釋能力方面優於隨機遊走填充基礎的去噪，並在多個金融指數 (包括但不限於 S&P 500、DJI 和 TWII) 上得到了驗證。

Stock price prediction constitutes a well-established area of research, with methods such as statistics or machine learning widely used in this field. Nevertheless, the natural noise in financial sequences poses challenges for both humans and computers. Fourier transform is effective for denoising in the frequency domain, but the issue of divergence presents a challenge. To address this divergence, previous approaches proposed using a random walk to construct padding data, isolating the divergence. However, the padding data generated by the random walk introduces noise, preventing the derivation of more coherent padding data and leading to an increased prediction error. In this study, we introduce a denoising technique based on stationary bootstrap padding and fast Fourier transform (SB-FTD). This method eliminates noise in the frequency domain and provides a more coherent approach to data padding. This method improves the random walk padding approach and allows denoising of the frequency domain characteristics of the original sequence in an environment that is not affected by noise. Our empirical results show that the proposed denoised approach outperforms random walk padding base denoising in terms of predictive ability and explanatory power with several financial indexes including but not limited to S&P 500, DJI, and TWII.

1 緒論...........1
2 研究方法.......4
3 實現 SB-FTD...17
4 資料來源......19
5 實驗結果......21
6 結論..........26
7 參考文獻......28

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