臺灣博碩士論文加值系統

我們研究AR(1)模型下的貝氏分析，在James O. Berger & Ruo-Yong Yang (1994)和Domenico Marinucci & Lea Petrella (1999)這兩篇文獻中為了比較事前分佈，皆各自提出新的事前分佈，認為其各自提出新的事前分佈是為佳事前分佈，因此在本篇論文中想驗證其事前分佈是否如其所言，並探討在本篇論文中所提出新的事前分佈是否也是個為佳的事前分佈。在本篇論文中利用事後分佈期望值之均方誤差及覆蓋機率來比較事前分佈，根據電腦模擬的結果，在本篇論文中的結果與 James O. Berger & Ruo-Yong Yang (1994)和Domenico Marinucci & Lea Petrella(1999)兩篇文獻幾近吻合，且在本篇論文中所提出新的事前分佈也會是個為佳的事前分佈。最後，根據O’Hagan (1995)所提出的事前分佈在穩定及非穩定的模式下進行模型篩選，其模擬的結果也會與Domenico Marinucci & Lea Petrella (1999)中幾近吻合，且在本篇論文中所提出新的事前分佈在穩定及非穩定的模式下也會有很好的結果表現。

We study the Bayesian analysis of AR(1) models. The priors discussed by James O. Berger & Ruo-Yong Yang (1994) and Domenico Marinucci & Lea Petrella (1999) are compared along with a new one which seems more appealing to us. Two criteria are used for the evaluation of the performance of the priors, i.e., the posterior mean square error (MSE) and frequentist coverage probability based on posterior quantiles. Our simulated results are in very close agreement with the results by James O. Berger & Ruo-Yong Yang (1994) and Marinucci & Lea Petrella (1999) for the priors considered by them. The new one, which we proposed here, seems to have a better performance than the others in view of the two criteria we used. Model selections between stationary and non-stationary models, proposed by O’Hagan (1995), is also considered for the priors. Results by Marinucci & Lea Petrella (1999) are duplicated, and we expect the new prior will demonstrate a better performance in terms of typeⅠand typeⅡerrors.

致 謝 ......................................................................Ⅰ
中文摘要.....................................................................Ⅱ
英文摘要.....................................................................Ⅲ
目 錄 ......................................................................Ⅳ
表目錄 ......................................................................Ⅵ
第壹章 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 研究步驟 ........................................................2
第貳章 文獻探討 ...........................................................4
第一節 AR(1)模式的介紹 .................................................4
第二節 貝氏推論 ........................................................7
第三節 相關文獻介紹.........................................................8
第參章 研究方法 ...........................................................16
第一節 事前分佈.........................................................16
第二節 概似函數.........................................................18
第三節 事後分佈 ........................................................19
第四節 理論介紹 ............................................................23
第肆章 電腦模擬與報表分析..................................................28
第一節 事前分佈之比較....................................................28
第二節 在AR(1)下的模型篩選..............................................41
第伍章 結論與建議..........................................................45
第一節 結論..............................................................45
第二節 建議.............................................................46
參考文獻.....................................................................47
表目錄
頁次
表1：事後分佈期望值的均方誤差................................................29
表2：0.05事後分佈百分位及0.95事後分佈百分位的覆遝鰷v........................32
表3：事後分佈期望值的均方誤差................................................38
表4：0.05事後分佈百分位及0.95事後分佈百分位的覆遝鰷v........................39
表5：在T=50中 在穩定及非穩定下占2000組觀察值的比率...........................42
表6：在T=90中 在穩定及非穩定下占2000組觀察值的比率...........................43

中文部分：
1. George E. P. Box & Gwilym M. Jenkin著，葉秋南譯，時間數列分
析-預測和控制，台北市：台灣銀行經濟研究室：中華書局經銷，
1984。
2. 吳柏林，時間數列分析導論，華泰書局，1995。
3. 吳喜之和謝邦昌，現代貝氏統計學及其應用，台北市：台灣知識
庫：鼎茂圖書出版有限公司經銷，2002。
英文部分：
1. Domenico Marinucci & Lea Petrella, “A Bayesian Proposal for the Analysis of Stationary and Nonstationary AR(1) Time Series”, Bayesian Statistics 6, Oxford：University Press, 1999, pp.821~828.
2. Douglas C. Montgomery, Lynwood A. Johnson, & John S. Gardiner,
Forecasting and Time Series Analysis, Singapore：McGraw-Hill, Inc,
second edition, 1990.
3. George E. P. Box & George C. Tiao, Bayesian inference in statistical
analysis, New York：Wiley, 1992.
4. Greta M. Ljung & George E. P. Box, “Analysis of Variance with Autocorrelated Observations”, Scandinavian Journal of Statistics 7, 1980, pp.172~180.
5. James O. Berger & Ruo-Yong Yang, “Noninformative priors and Bayesian testing for the AR(1) model”, Econometric Theory 10, 1994, pp. 461~482.
6. John Geweke, “Bayesian inference in econometric models using Monte Carlo integration”, Econometrica 57, 1989, pp.1317~1339.
7. Kloek, T. & Van Dijk, H.K., “Bayesian estimates of equation system parameters : An application of integration by Monte Carlo”, Econometrica 46, 1978, pp.1~20.
8. O’Hagan, A, “Fractional Bayes factors for model comparison.”, Journal of Royal Statistical Society B 57, 1995, pp.99~138.