在本文中我們利用貝氏方法來選取GARCH或 門檻 GARCH 的最適模式。先利用貝氏方法對參數的後驗分配作推論,以馬可夫鏈蒙第卡羅法 (Makov chain Monte Carlo methods)對參數進行疊代估計,其中包含隨機漫步 Metropolis-Hastings 演算法與Independent Kernel Metropolis-Hastings 演算法。再應用Green(1995)所提出的可逆跳躍式馬可夫鏈蒙第卡羅法(Reversible jump Makov chain Monte Carlo methods)來比較 GARCH 與 門檻 GARCH 模式,並選取最適當的模式。

本文中透過選取模式中參數alpha_0不同區間長度的事前分配,不同條件變異數與不同資料長度的組合的模擬來檢驗我們所提的方法。
本研究方法也應用在十個國際股票市場股價日報酬率資料的分析上,其中包含屬於歐美國家的英國倫敦金融時報百種指數(FTSE 100),加拿大多倫多300種綜合指數(TSE 300 Composite),德國法蘭克福 DAX 指數(DAX 30 stocks),美國 S & P 500 指數(Standard & Poor 500 Index) 與美國那斯達克指數(NASDAQ Composite)。
以及屬於亞洲國家的日本日經225指數(NIKKEI 255),
香港恆生指數(Heng Seng Index),新加坡海峽時報指數(Straits Time),韓國漢城綜合指數(SE Composite)與
台灣加權股價指數(Taiwan Weighted)。
研究這十個國際股票市場的日報酬率適合選用何種模式來配適,並觀察各市場是否有非對稱性的波動現象。
結果中我們發現有顯著的證據支持投資報酬率的波動函數為非對稱之假設。

第1章 緒論.........................1
第2章 模型建立與貝氏推論...........6
2.1 模型建立.................7
2.2 貝氏推論.................9
第3章 馬可夫鏈蒙地卡羅法(MCMC Methods).......................... 13
3.1 吉氏抽樣法(Gibbs sampler)與 Metropolis- Hastings 演算法........ 13
3.2 可逆跳躍式馬可夫鏈蒙地卡羅法 (Reversible Jump MCMC Methods)..... 17
3.3 研究方法.................19
第4章 模擬研究與實例分析...........24
4.1 Simulated series.........25
4.2 Simulation study.........28
4.3 實例分析.................32
第5章 結論與未來研究方向...........35
參考文獻...........................38
附錄 (表、圖)......................43

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