跳到主要內容

臺灣博碩士論文加值系統

(3.237.6.124) 您好!臺灣時間:2021/07/24 02:29
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:黃慧釧
研究生(外文):Huei-Chuan Huang
論文名稱:連續型自迴歸時間模式之貝氏分析應用
論文名稱(外文):On Continuous Time Threshold Autoregressive Model : a BayesianApplication
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:2006
畢業學年度:94
語文別:中文
論文頁數:44
中文關鍵詞:Girsanov’s formula布朗橋貝氏方法隨機方程式
外文關鍵詞:Brownian Bridgestochastic differentialBayesian methodGirsanov’s formula
相關次數:
  • 被引用被引用:0
  • 點閱點閱:173
  • 評分評分:
  • 下載下載:26
  • 收藏至我的研究室書目清單書目收藏:0
對於連續型非線性的時間序列模型在時間序列的分析上有著相當重要的應用,但通常其概似函數卻無法獲得, 因此在分析上就會比線性的模型困難許多。
一些文獻當中, 例如: Tong (1983), Tsay (1986, 1989),Tong and Yeung (1991), Brockwell, Liu and Tweedie (1992),對於非線性的模型已有所討論。
在此篇論文當中, 我們根據 Roberts and Stramer (2001) 及 Lin (2003) 利用貝氏統計方法對連續型時間門檻自迴歸過程 (continuous time threshold autoregressive model) 做分析。
在應用上, 我們套用的是 S&P 500 的資料,其為一個從 1994 年 1 月 3 日為期約兩年的股市交易收盤指數。 在先前的文獻當中,都是對資料時間間隔為相等的 (equally spaced data) 來做探討,但在實務上,我們能夠得到的資料往往與等間隔的時間間隔此項假設不符,
因此本文將改正這樣的假設,針對整個過程中造成不等的時間間隔的遺失資料作處理。
The non-linear continuous time models have important applications in time series analysis. However, their likelihood functions are usually not available. As a result, the analysis is trickier than that of their discrete time conunterparts.
In this study, we use the Bayesian method to analyze the continuous time threshold autoregressive models. This approach is
based on Roberts and Stramer (2001) and Lin (2003). In the applications to financial data S&P 500, we assume the daily data are not equally spaced since the stock market only opens on weekdays and we treat the paths between observed data are missing.
Contents
1.序論........................................................7
1.1 Gibbs 演算法 與 Metropolis-Hastings 演算法..............9
1.2 隨機過程 (Stochastic Process)...........................12
1.3 布朗運動 (Brownian Motion) 與布朗橋 (Brownian Bridge)...14
1.4 隨機積分 (Stochastic Integrals).........................16
2.時間序列模型介紹 與 研究方法................................19
2.1 時間序模型介紹..........................................19
2.2 研究方法................................................23
3.實例驗證....................................................33
3.1 CAR(1) 模型 ............................................33
3.2 CTAR(1) 模型............................................35
4.結論........................................................39
作者簡介......................................................44

List of Figures
1.1 The pathes of stochastic process with different w.........14
1.2 Brownian Motion and Brownian Bridge.......................16
2.1 假設在四個時間點觀測到的觀測值以星號表示..................28
2.2 假設 h=0.5, 星號為觀測值, 三角記號為補充的資料............28
3.1 a0,a1 MCMC Outputs 時間圖形...............................34
3.2 r, sigma^2 MCMC Outputs 時間圖形..........................36
3.3 a10, a11 MCMC Outputs 時間圖形............................37
3.4 a20, a21 MCMC Outputs 時間圖形............................38
[1] Brockwell, P., Liu, J. and Tweedie, R.L. (1992) On the existence
of stationary threshold autogressive moving-average processes. J.
Time Ser. Anal. 13, 95-107.
[2] Brockwell, P.J. (1994), On continuous-time threshold ARMA processes.
J. Statist. Planning Inf.,39, 291–303.
[3] Brockwell, P.J. (2001), Continuous-time ARMA Processes, In
Stochastic Processes, Theory and Methods, Handbook of Statistics
19, eds. D.N. Shanbhag and C.R. Rao, Elsevier, Amsterdam, 249-
276.
[4] Chib, S. and Jeliazkov, I. (2001), Marginal likelihood from the
Metropolis-Hastings output. J. Amer. Statist. Assoc., 96, 270–281.
[5] Green, P. J. (1995), Reversible jump Markov chain Monte
Carlo computation and Bayesian model determination. Biometrika,
82(4), 711–732.
[6] Lin, Y. (2003), The Bayesian Analysis of Threshold Autoregressive
Models, Ph.D. dissertation, The University of Iowa.
[7] Oksendal, B. (2003), Stochastic Differential Equations, 6th ed.,
Springer
[8] Ox ( a C++ like matrix language), avaiable to be downloaded at
http://www.doornik.com .
[9] Stramer, R. L. Tweedie and P. J. Brockwell (1996), Existence and
stability of continuous time threshold ARAM process, Statistica
Sinica, 6, 715–732.
[10] Roberts, G.O. and Stramer, O.(2001), On inference for partially
observed non-linear diffusion models using the Metropolis-Hastings
algorithm. Biometrika, 1, 47–71.
[11] Tanner, A. , Wong, W. (1987) The Calculation of Posterior Distributions
by Data Augmentation Journal of the American Statistical
Association, Vol. 82, No. 398. , pp. 528-540.
[12] Thomas Bj¨ork. (1998) ”Arbitrage Theorey in Continuous Time”
OXFORD.
[13] Thomas Milkosch (1998) ”Elementary stochastic calculus with Finance
in View” World Scientific.
[14] Tong, H. (1983), Threshold models in non-linear time series analysis.
Vol. 21 of Lecture Notes in Statistics (ed. K. Krickegerg), New York:
Spring-Verlag.
[15] Tong, H. and Yeung. I. (1991), Threshold autogressive modeling in
continuous time. Statistics Sinica,1, 411-430.
[16] Tsai, H. and Chan, K.S. (1999) A new EM method for estimating
continuous–time Autoregressive models. Technical report, Dept. of
Statistics and Actuarial Science, U. of Iowa, No. 285.
[17] Tsai, H. and Chan, K.S. (2000a), Testing for nonlinearity with partially
observed time series. Biometrika, 87(4), 805–821
[18] Tsay, R. S. (1986). Nonlinearity test for time series. Biometrika, 73,
461-66.
[19] Tsay, R. S. (1989). Testing and modeling threshold autogressive
process. J. Am. Stastic Assoc. 84, 231-40.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top