臺灣博碩士論文加值系統

波動性的預測近年來一直學者們關心的焦點。傳統GARCH模型解釋了資產報酬率的異質變異情況，但由於實際變異數無法觀察，以致無法確切的描繪真實波動性的現象。Chou (2005)提出CARR（Conditional Autoregressive Range）模型，探討變幅與時而變的動態過程，並提出指數分配、韋伯分配皆可做為變幅的分配設定。本文以CARR模型為基礎，改變分配為指數、韋伯與伽瑪分配，以臺灣加權股價指數為資料進行分析，比較不同分配設定下CARR的差異。另將CARR與GARCH結合，試圖獲取較佳的樣本外預測結果，並比較Range-based GARCH與Return-based GARCH對於報酬與波動性預測能力的優劣。實證結果顯示，伽瑪分配在配適上是較佳的分配設定，另外透過樣本外預測力比較，GARCH-CARR比傳統GARCH模型具有較好的預測能力。

In recent decades, many studies have focused on the forecasting of volatility. The GARCH model provides the heteroskedasticity of the asset returns. But estimating the volatility can be difficult, because volatility is not observable. Chou(2005) proposed CARR (Conditional Autoregressive Range) model to explain the time-varying of range. In this study, We use CARR model by using TAIEX index data from 1999 to 2011, to compare different distribution (exponential, Weibull and Gamma distribution). And combine the CARR model and GARCH model, to compare the out-of-sample forecasts of Range-based GARCH and Return-based GARCH. We find the Gamma distribution is the best of those assumptions. And GARCH-CARR model provides the better prediction of volatility.

摘要 I
ABSTRACT II
誌謝辭 III
第一章　前言 1
第二章　文獻回顧 3
第三章　研究方法 8
第一節　GARCH模型 8
第二節　CARR模型 9
第三節　AR-GARCH-CARR模型 13
第四章　資料分析 15
第一節　資料選取 15
第二節　資料特性 15
第五章　實證分析 18
第一節　CARR模型參數結果與分析 18
第二節　AR-GARCH-CARR模型參數結果與分析 24
第三節　樣本外預測 26
第六章　結論 29
參考文獻 30

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