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研究生:郭倉瑋
研究生(外文):cang-wei guo
論文名稱:高斯混合時間序列模型:分析與計算
指導教授:黃愉閔
學位類別:碩士
校院名稱:東海大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
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
中文關鍵詞:高斯混合轉換分佈ARIMA模型EM演算法貝氏分析Gibbs sampler
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時間序列模型的選取一直是時間序列分析的一個重要關鍵,而在本文當中闡述了Le, N.D., Martin, R.D. and Raftery, A.E. (1996)所提出的高斯混合轉換分佈(GMTD)模型,發現其模型利用了將數個常態分配混合的動作,使得模型更具有彈性,並在本文中藉由電腦模擬的結果比較GMTD模型以及ARIMA模型對於時間序列資料的配適結果;另外,提出一貝氏估計方法,採用Gibbs sampler以求得模型的參數估計值,也希望藉此改善EM演算法可能碰到的問題。
第一章、緒論……………………………………………………………3
第二章、模型描述與選取………………………………………………5
第一節、模型介紹…………………………………………………5
第二節、模型性質…………………………………………………6
第三節、模型選取…………………………………………………8
第三章、分析方法-EM演算法…………………………………………9
第四章、資料分析………………………………………………………16
第五章、貝氏估計方法…………………………………………………19
第一節、模型概要…………………………………………………19
第二節、Gibbs sampler…………………………………………26
第六章、結論……………………………………………………………29
附錄…………………………………………………………………….30
參考文獻……………………………………………………………….32
Adrian E. Raftery (1985) A Model for High-Order Markov Chains. Journal of the Royal Statistical Society. Series B (Methodological), Vol. 47, No. 3, pp. 528-539
Adrian E. Raftery and Simon Tavare (1994). Estimation and modelling repeated
patterns in high-order Markov chains with the mixture transition distribution
(MTD) model. Applied Statistics 43: 179-200.
A.P. Dempster, N. M. Laird, and D. B. Rubin (1977), "Maximum likelihood from incomplete data via the EM algorithm," J. Royal Stat. Soc., vol. 39, pp. 1--38,
Akaike, H. (1973). Information Theory and an Extension of the Maximum Likelihood Principle, in the Second International Symposium on Information Theory, eds. B. N. Petrov and F. Csake, Hungary:Akademiai Kiado, pp. 267-281 .
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the Metropolis algorithm. Illinois J. Math. v50. 67-91.
Box, G. E. P.,and Jenkins, G. M. (1976), Time Series Analysis Forecasting and Control, (2nd ed.), San Francisco:Holden-Day .
Engle, R. F. (1982) Autoregressive Conditional Heteroskedasticity With Estimates of
The Variance of U.K Inflation, Econometrica, 50, 987-1008 .
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Le, N.D., Martin, R.D. and Raftery, A.E. (1996) Modeling outliers, bursts and flat
stretches in time series using mixture transition distribution (MTD) models.
Journal of the American Statistical Association, 91: 1504-1515.
LIU, J. (1996). Metropolized independent sampling with comparisons to re-
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Martin, R. D., and Raftery, A. E . (1987). Robustness, Computation, and Non- Euclidean Models. Journal of the American Statistical Association, 82, 1044-1050 .
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