本論文探討動態受限因子模型在高維度時間序列資料上的應用。在模式設定上，有別於藉由主觀訊息預先設定受限矩陣，本研究將sparse fused lasso的技巧引入最大概似估計式中，透過參數估計並搭配集群分析與群數選取指標，利用資料訊息決定模式中受限矩陣的結構，以達到簡化高維度時間序列建模的目的。模擬研究顯示所提出之方法，在簡化模式結構上頗具成效，此方法已成功地運用在財務相關之實例分析。

摘　要 i
Abstract ii
致謝詞 iii
目錄 iv
圖表目錄 vi
1. 緒論 1
2. 受限因子模型 3
3. 參數估計 5
3.1 概似函數（likelihood function） 5
3.2 以EM演算法求MLE解 6
EM演算法的步驟 8
3.3 Sparse fused lasso approach (SFL) 8
Sparse fused lasso參數估計 10
Sparse fused lasso演算法 11
4. 決定受限矩陣Ｈ 11
4.1 集群分析 11
4.2 奇異值分解 12
4.3 兩種決定 H 之演算法 13
演算法I：MLE via Sparse fused法 13
演算法II：數據矩陣 via SVD法 14
5. 模型維度選取 16
5.1 決定因子個數 16
5.2 決定受限個數 17
CH index 18
KL index 18
H 統計量 19
6. 模擬分析 19
6.1 低維度下選取受限結構 20
6.2 高維度下選取受限結構 32
6.3 選取局部受限結構 33
7. 實例分析 35
7.1 股票報酬率數據分析 36
7.2 空氣品質的數據分析 37
8. 結論 40
參考文獻 41
附錄- Sparse fused lasso approach 43
Sparse fused參數估計 43
Sparse fused演算法 44

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