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姓名 錢衍成(Yan-Cheng Chien)  查詢紙本館藏   畢業系所 統計研究所
論文名稱 門檻隨機波動跳躍模型之貝氏推論
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摘要(中) 本文考慮門檻隨機波動模型與門檻隨機波動跳躍模型之貝氏分析。在給定主觀先驗分佈下,以馬可夫鏈蒙地卡羅方法估計模型中之未知參數,進而討論未來觀測值與風險值之預測。關於隨機跳躍部份,本文亦分別考慮跳躍幅度與跳躍機率可能會隨門檻值改變的情形。實務分析中,可以 DIC 準則做為模型選擇的依據。
摘要(英) This thesis presents a threshold stochastic volatility model and a threshold stochastic volatility jump model with unknown threshold from a Bayesian viewpoint. Bayesian inferences of the unknown parameters are obtained with respect to a subjective prior distribution via Markov chain Monte Carlo (MCMC) method.
In addition, the value at risk (VaR) of the distribution of the next future observation is also developed based on predictive distribution. For jump component in the threshold stochastic volatility model, we consider the situations where the jump size and jump probability might be changed by the threshold value. In practice, the deviance information criterion (DIC) is suggested for model selection.
關鍵字(中) ★ 門檻隨機波動模型
★ 主觀先驗分佈
★ 馬可夫鏈蒙地卡羅
★ 風險值
★ 門檻隨機波動跳躍模型
★ DIC 準則
關鍵字(英) ★ threshold stochastic volatility model
★ Markov chain Monte Carlo (MCMC)
★ Bayesian
★ deviance information criterion (DIC)
論文目次 第一章緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01
1.1 研究背景與動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01
1.2 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 02
1.3 研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 06
第二章門檻隨機波動模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 08
2.1 門檻隨機波動模型參數之貝氏估計. . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 風險值之估計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
第三章門檻隨機波動跳躍模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 門檻隨機波動跳躍模型I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 門檻隨機波動跳躍模型I 參數之貝氏估計. . . . . . . . . . . . . . . 23
3.1.2 門檻隨機波動跳躍模型I 之風險值估計. . . . . . . . . . . . . . . . . 27
3.2 門檻隨機波動跳躍模型II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 門檻隨機波動跳躍模型II 中參數之貝氏估計. . . . . . . . . . . . 28
3.2.2 門檻隨機波動跳躍模型II 之風險值估計. . . . . . . . . . . . . . . . 30
3.3 門檻隨機波動跳躍模型III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
第四章模擬研究. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1 門檻隨機波動模型之模擬. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 門檻隨機波動跳躍模型I 之模擬. . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 門檻隨機波動跳躍模型II 之模擬. . . . . . . . . . . . . . . . . . . . . . . . 36
4.4 門檻隨機波動跳躍模型III 之模擬. . . . . . . . . . . . . . . . . . . . . . . 37
4.5 模型選擇. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
第五章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
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指導教授 樊采虹(Tsai-Hung Fan) 審核日期 2007-7-19
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