由於金融資產具有波動叢聚與異質變異的特性，欲估計出真實波動度而言是相當困難的，故本研究擬使用善於捕捉金融資產波動叢聚與異質變異能力之GARCH模型架構下，考慮二類波動模型：（1） GARCH（1,1）模型、（2） 在GARCH的條件變異數方程式中分別加入日變幅（PK、GK與RS）、已實現波動（Realized volatility, RV）、已實現雙冪次變異（Realized bipower variation, RBP）、隱含波動（Implied volatility, IV）與隔夜波動（Overnight volatility, ONV）之增廣GARCH模型，進行台灣加權股價指數（TWSE）與台灣櫃檯指數（OTC）日報酬率之波動預測，探討隱含於各波動估計式的日/日內價格交易資訊能否提升GARCH模型的波動預測能力。本研究在實證上擬以絕對報酬率（Absolute returns, ARET）、 PK日變幅與5分鐘之RV作為真實波動代理變數。在MAE及LL二種損失函數中，使用三種波動代理變數來建構樣本外波動預測績效的評估。特別是，本研究進一步使用benefit統計方法來檢測七種波動估計式對提升GARCH模型之波動預測的訊息價值。實證結果顯示，除了以ARET為波動代理變數之預測績效結果外，PK與RV之預測績效結果幾乎一致，皆以GARCH-RBP模型之預測能力最佳，即對GARCH模型能提升較多的波動預測之準確性。

Estimating the true volatility of assets returns is a difficult task since financial assets are well known to have stylized characteristics of volatility clustering and heteroskedasticity. Based on the GARCH （generalized autoregressive conditional heteroskedasticity, GARCH） framework, this thesis considers two GARCH volatility model specifications: （i） the traditional GARCH（1,1） model, （ii） the GARCH-X model which augments the traditional GARCH model by respectively incorporating daily price ranges （PK, GK, and RS）, realized volatility （RV）, realized bipower variation （RBP）, implied volatility and overnight volatility （ONV） as explanatory variable into the GARCH variance equation. These models are used to investigate the information value of the daily/intraday trading prices that is embodied in the aforementioned volatility estimators for improving forecasts of TWSE and OTC stock markets volatilities at daily horizon. This study adopts ARET （absolute returns）, PK range and RV volatility proxy measures for used in empirical exercise. The out-of-sample forecast evaluation is conducted using various proxy measures in terms of MAE and LL loss error statistics. Particularly, this study also employs benefit statistics to further examine the information values of the various estimators for improving GARCH-based volatility forecasts. The empirical results show that to predict fluctuations in performance results of the ARET proxy variables except, both the prediction of PK and RV performance results are almost the same, the predictive power of the model begin with GARCH-RBP are the best, i.e. GARCH model can enhance more accuracy of the volatility forecasting.

目 錄
第一章 緒論	1
第一節 研究背景與動機	1
第二節 研究目的	3
第三節 研究架構	4
第四節 研究流程圖	5
第二章 理論基礎與文獻回顧	6
第一節 波動估計式	8
第二節 波動估計模型：GARCH	9
第三節 波動預測相關文獻	10
1.每日波動預測文獻	10
2.日內波動預測文獻	12
第四節 波動在財務應用之相關文獻	14
1.波動估計式應用在風險值與避險之相關文獻	15
2.波動估計式應用在投資組合之相關文獻	18
3.波動估計式應用在選擇權價格預測之相關文獻	19
第三章 研究方法	22
第一節 單根檢定	22
1.ADF（Augmented Dickey-Fuller）單根檢定方法	22
2.PP（Phillips-Perron）單根檢定方法	23
第二節 波動估計式	24
1.隔夜波動	24
2.PK日變幅	24
3.GK日變幅	25
4.RS日變幅	25
5.已實現波動	25
6.已實現雙冪次變異	26
7.波動率指數	26
第三節 GARCH模型架構	27
第四節 損失函數	28
第四章 資料與實證分析	29
第一節 資料來源及處理	29
1.實證資料	29
2.資料來源	29
3.資料處理	30
第二節 基本統計分析	32
第三節 單根檢定	38
第四節 實證結果	41
1.以ARET為波動代理變數	42
2.以PK日變幅為波動代理變數	46
3.以RV為波動代理變數	50
第五章 結論	55
參考文獻	57


表目錄
表1. 過去文獻使用的波動代理變數之彙總	21
表2. 台灣加權股價指數與台灣櫃檯指數之相關訊息	29
表3. 台灣加權股價指數日報酬率之基本統計特性	32
表4. 台灣櫃檯指數日報酬率之基本統計特性	32
表5. 各波動估計式之基本統計特性（台灣加權股價指數）	35
表6. 各波動估計式之基本統計特性（台灣櫃檯指數）	35
表7. 台灣加權股價指數與台灣櫃檯指數之單根檢定	39
表8. 台灣加權股價指數與台灣櫃檯指數日報酬之單根檢定	40
表9. 樣本外波動性預測績效比較（以ARET為代理變數）	43
表10. 波動估計式對波動性預測的資訊價值（以ARET為波動代理變數）	45
表11. 樣本外波動性預測績效比較（以PK為代理變數）	47
表12. 波動估計式對波動性預測的資訊價值（以PK為波動代理變數）	49
表13. 樣本外波動性預測績效比較（以RV為代理變數）	51
表14. 波動估計式對波動性預測的資訊價值（以RV為波動代理變數）	53


圖目錄
圖1. 研究架構流程圖	5
圖2. 台灣加權股價指數之時間序列資料走勢圖	33
圖3. 台灣加權股價指數報酬率之時間序列資料走勢圖	33
圖4. 台灣櫃檯指數之時間序列資料走勢圖	34
圖5. 台灣櫃檯指數報酬率之時間序列資料走勢圖	34
圖6. 台灣加權股價指數之各種波動估計式之圖形	36
圖7. 台灣櫃檯指數之各種波動估計式之圖形	37
圖8. 移動視窗估計方法	41

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