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研究生:林均豪
研究生(外文):Chun-Hao Lin
論文名稱:自迴歸GARCH模型之貝氏模型選擇
論文名稱(外文):A Bayesian Model Selection of AR-GARCH Models Using the Reversible Jump MCMC Approach
指導教授:林余昭
指導教授(外文):Yu-Jau Lin
學位類別:碩士
校院名稱:中原大學
系所名稱:應用數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:67
中文關鍵詞:GARCH modelAR modelMetroplis–Hastings algorithmReversible Jump Markov Chain Monte Carlo
外文關鍵詞:Reversible Jump Markov Chain Monte CarloMetroplis–Hastings algorithmAR modelGARCH model
相關次數:
  • 被引用被引用:3
  • 點閱點閱:296
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  • 收藏至我的研究室書目清單書目收藏:0
  時間序列模型在財務金融分析上有著相當重要的應用,但其概似函數通常無法求得,因此在分析時就會比線性模型困難許多。在金融的時間序列上,一般化自我迴歸條件異質變異數分析模型 (GARCH 模型) 已經被廣泛應用,通常用來研究具有波動性的資料。
  馬可夫鏈蒙地卡羅法 (MCMC 法) 成功地應用在估計 GARCH 模型的參數,而且可逆跳躍式馬可夫鏈蒙地卡羅法 (RJMCMC 法) 可以更進一步解決模型選擇的問題,使得吉氏抽樣法 (Gibbs sampling) 能夠突破以往的限制,在不同空間的模型作參數估計。
  在本篇論文中,我們假設 AR-GARCH 模型的階次皆是未知的,所有的參數都可以利用貝氏方法來估計,我們運用統計軟體讓資料在 AR-GARCH 模型中選擇一個最好的模型。
  最後,我們將此方法應用在台灣加權股價指數的收盤指數,選擇的資料從 2005/01/01 到 2009/05/31,共計 1,088 筆,在這組資料下,我們得到最好的配適模型是 AR(1)-GARCH(1,1) 模型。
The time series models have important applications in financial analysis. However, their likelihood functions are usually not available in the explicit form. Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models capture certain characteristics commonly associated with financial time series, they give a statistical way of representing the changing volatility of data. And the estimation of such models has intensively and successfully been studied.
Markov Chain Monte Carlo (MCMC) method has been successful in estimating the parameters of GARCH models. Moreover, the Reversible Jump Markov Chain Monte Carlo (RJMCMC) method is employed to solve the model selection problem. It enables the Gibbs sampling schemes to work in different spaces.
In this research, we assume the orders of both AR and GARCH parts in the models are unknown and the corresponding parameters are to be estimated using the Bayesian approach. That is, we provide a procedure that automatically chooses the best one among AR-GARCH models.
Finally, this technique is applied to real data (Taiwan stock index, 2005/01/01-2009/05/31) and the best model is AR(1)-GARCH(1,1).
目錄
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . I
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . II
謝誌. . . . . . . . . . . . . . . . . . . . . . . . . . . . . III
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . VI
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII
1 緒論
1.1 研究目標. . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究方法. . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . 7
2 模型介紹
2.1 AR 模型. . . . . . . . . . . . . . . . . . . . . . . . . .8
2.2 MA 模型. . . . . . . . . . . . . . . . . . . . . . . . . .8
2.3 ARCH 模型. . . . . . . . . . . . . . . . . . . . . . . . .8
2.4 GARCH 模型. . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 AR-GARCH 模型. . . . . . . . . . . . . . . . . . . . . . .9
3 研究方法
3.1 馬可夫鏈蒙地卡羅法. . . . . . . . . . . . . . . . . . . . 12
3.2 吉氏抽樣法. . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Metropolis–Hastings 演算法. . . . . . . . . . . . . . . .14
3.4 可逆跳躍式馬可夫鏈蒙地卡羅法. . . . . . . . . . . . . . . 15
4 模擬研究與實例分析
4.1 模擬研究. . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 實例分析. . . . . . . . . . . . . . . . . . . . . . . . 45
5 結論以及未來之研究方向. . . . . . . . . . . . . . . . . . 51
6 參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . 52


圖目錄
1 模擬資料1長度為2000之時間序列圖, ACF 圖及PACF 圖19
2 模擬資料2長度為2000之時間序列圖, ACF 圖及PACF 圖20
3 模擬資料3長度為2000之時間序列圖, ACF 圖及PACF 圖21
4 模擬資料4長度為2000之時間序列圖, ACF 圖及PACF 圖22
5 模擬資料1配適模型的前200次時間序列圖(RJMCMC 法) 30
6 模擬資料2配適模型的前200次時間序列圖(RJMCMC 法) 30
7 模擬資料3配適模型的前200次時間序列圖(RJMCMC 法) 31
8 模擬資料4配適模型的前200次時間序列圖(RJMCMC 法) 31
9 模擬資料1配適模型的時間序列圖(RJMCMC 法) . . . . . 32
10 模擬資料1配適模型的直方圖. . . . . . . . . . . . . . . . 32
11 模擬資料2配適模型的時間序列圖(RJMCMC 法) . . . . . 33
12 模擬資料2配適模型的直方圖. . . . . . . . . . . . . . . . 33
13 模擬資料3配適模型的時間序列圖(RJMCMC 法) . . . . . 34
14 模擬資料3配適模型的直方圖. . . . . . . . . . . . . . . . 34
15 模擬資料4配適模型的時間序列圖(RJMCMC 法) . . . . . 35
16 模擬資料4配適模型的直方圖. . . . . . . . . . . . . . . . 35
17 模擬資料1配適AR(1)-GARCH(1,1) 模型, MCMC 迭代
樣本參數之時間序列圖, line 表正確值. . . . . . . . . . . 37
18 模擬資料1配適AR(1)-GARCH(1,1) 模型, MCMC 迭代
樣本參數之ACF 圖. . . . . . . . . . . . . . . . . . . . 38
19 模擬資料2配適AR(1)-GARCH(2,2) 模型, MCMC 迭代
樣本參數之時間序列圖, line 表正確值. . . . . . . . . . . 39
20 模擬資料2配適AR(1)-GARCH(2,2) 模型, MCMC 迭代
樣本參數之ACF 圖. . . . . . . . . . . . . . . . . . . . 40
21 模擬資料3配適AR(2)-GARCH(1,1) 模型, MCMC 迭代
樣本參數之時間序列圖, line 表正確值. . . . . . . . . . . 41
22 模擬資料3配適AR(2)-GARCH(1,1) 模型, MCMC 迭代
樣本參數之ACF 圖. . . . . . . . . . . . . . . . . . . . 42
23 模擬資料4配適AR(2)-GARCH(2,2) 模型, MCMC 迭代
樣本參數之時間序列圖, line 表正確值. . . . . . . . . . . 43
24 模擬資料4配適AR(2)-GARCH(2,2) 模型, MCMC 迭代
樣本參數之ACF 圖. . . . . . . . . . . . . . . . . . . . 44
25 轉換後的收盤指數之時間序列圖, ACF 圖及PACF 圖. . . 46
26 實際資料配適AR(1)-GARCH(1,1) 模型, MCMC 迭代
樣本參數之時間序列圖. . . . . . . . . . . . . . . . . . . 49
27 實際資料配適AR(1)-GARCH(1,1) 模型, MCMC 迭代
樣本參數之ACF 圖. . . . . . . . . . . . . . . . . . . . 50


表目錄
1 模擬資料1的樣本統計量. . . . . . . . . . . . . . . . . . 19
2 模擬資料2的樣本統計量. . . . . . . . . . . . . . . . . . 20
3 模擬資料3的樣本統計量. . . . . . . . . . . . . . . . . . 21
4 模擬資料4的樣本統計量. . . . . . . . . . . . . . . . . . 22
5 模擬資料1配適各個模型的參數估計值. . . . . . . . . . . 26
6 模擬資料2配適各個模型的參數估計值. . . . . . . . . . . 26
7 模擬資料3配適各個模型的參數估計值. . . . . . . . . . . 27
8 模擬資料4配適各個模型的參數估計值. . . . . . . . . . . 27
9 模擬資料1配適AR(1)-GARCH(1,1) 模型的參數估計值. 45
10 模擬資料2配適AR(1)-GARCH(2,2) 模型的參數估計值. 45
11 模擬資料3配適AR(2)-GARCH(1,1) 模型的參數估計值. 45
12 模擬資料4配適AR(2)-GARCH(2,2) 模型的參數估計值. 45
13 轉換後的收盤指數之樣本統計量. . . . . . . . . . . . . . 46
14 ADF 檢定法. . . . . . . . . . . . . . . . . . . . . . . 46
15 Q 統計量之p-value 結果. . . . . . . . . . . . . . . . . 47
16 實際資料迭代RJMCMC 法之結果. . . . . . . . . . . . 47
17 各模型之AIC 值. . . . . . . . . . . . . . . . . . . . . 47
18 實際資料配適AR(1)-GARCH(1,1) 模型的參數估計值. . 48
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