波動性在財務上扮演著關鍵的角色，若能適當的描述波動性模型，將有助於投資組合配置的最適化，進而能有效的控管風險。GARCH模型在波動性的預測上已被廣泛的應用，而且也能在實證上得到良好的成效。然而Chou (2005)將GARCH 模型結合變幅在波動性預測上的優勢進一步提出條件變幅自我相關(Conditional Auto-Regressive Range，CARR)模型，並且在S&P500 股價指數波動性預測實證上獲得優於GARCH模型的結論。本文中將介紹CARR 模型及其性質，並以日圓與星幣為研究對象，分別進行CARR 模型和Skew-t GARCH 模型在樣本內及樣本外波動性的預測能力比較；結果與Chou (2005)認為CARR模型對股價指數波動有較佳的預測結果相異。故認為CARR模型在預測波動性上並非具有完全的優勢，不同商品應適用不同的模型進行預測，以期得到最適的預測波動性，提升投資決策的效率。

In finance, volatility plays a key role in several sub-fields. Whether the construct
of portfolio is optimal or not, partly depends on the control of volatility. GARCH family models have been used in the forecast of volatilities, and have performed well in many empirical studies. Recently, Chou (2005) proposed the CARR
(Conditional Auto-Regressive Range) model. The main concept of the CARR model is to use a simple dynamic structure for range to characterize the volatility process. In Chou (2005), comparing the CARR model and traditional GARCH model, the former is better in the volatility forecasting based on the data of the S&P 500 index. We use both CARR and GARCH models to test JPY and SGD exchange rate. But we find that different data uses different models. In order to obtain the most accurate projection of volatility and improve the decision-making efficiency, it’s better to apply specific volatility forecast models to different products.

第一章緒論 	1
第一節研究背景與動機	1
第二節研究目的 	2
第三節研究架構	3
第四節研究流程	5
第二章文獻探討與回顧	6
第一節波動性預測模型	6
第二節波動性模型發展與預測能力比較的文獻	6
第三章研究方法	11
第一節模型的介紹	11
一、GARCH	         11
二、AR(1)-GARCH	12
三、EGARCH	13
四、GARCH-M	14
五、Skew-t GARCH	15
六、CARR模型	15
第二節預測能力的比較	21
一、樣本外預測能力的比較	21
二、樣本內預測能力的比較	23
第四章樣本資料分析	         25
第一節樣本資料與取樣期間	25
第二節樣本資料的基本統計分析	25
第五章實證結果分析	31
第一節ECARR模型與WCARR模型的參數估計	31
一、ECARR模型的參數估計	31
二、WCARR模型的參數估計	34
第二節WCARR模型與Skew-t GARCH模型樣本外預測能力的比較	38
第三節Skew-t分配下的GARCH族模型的實證比較	43
第六章結論	50
參考文獻	  	51

表目錄	
表1   日圓、星幣樣本資料	25
表2-1 日圓匯率週資料之報酬率、絕對報酬率、與變幅之基本統計量	27
表2-2 星幣匯率週資料之報酬率、絕對報酬率、與變幅之基本統計量	29
表3-1 日圓匯率的ECARR模型的參數估計	33
表3-2 星幣匯率的ECARR模型的參數估計	33
表4-1 日圓匯率的WCARR模型的參數估計	35
表4-2 星幣匯率的WCARR模型的參數估計	35
表6-1 日圓匯率的WCARR與Skew-t GARCH之樣本外預測	39
表6-2 星幣匯率的WCARR與Skew-t GARCH之樣本外預測	40
表7-1 日圓匯率週資料的WCARR與Skew-t GARCH之樣本外預測能力比較	42
表7-2 星幣匯率週資料的WCARR與Skew-t GARCH之樣本外預測能力比較	43
表8-1 日圓匯率Skew-t 分配下的GARCH、GARCH-M與AR(1)-GARCH之樣本外預測	44
表8-2 星幣匯率Skew-t 分配下的GARCH、GARCH-M與AR(1)-GARCH之樣本外預測	45
表9-1 日圓匯率週資料的Skew-t 分配下的GARCH、GARCH-M、AR(1)-GARCH樣本外預測能力比較	47
表9-2 星幣匯率週資料的Skew-t 分配下的GARCH、GARCH-M、AR(1)-GARCH樣本外預測能力比較	48

圖目錄
圖1   研究流程	5
圖2-1 日圓匯率變幅與報酬率的走勢圖	28
圖2-2 星幣匯率變幅與報酬率的走勢圖	30
圖3-1 日圓匯率之ECARR(1,1) 與WCARR(1,1)的殘差機率密度圖	36
圖3-2 星幣匯率之ECARR(1,1) 與WCARR(1,1)的殘差機率密度圖	37

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