跳到主要內容

臺灣博碩士論文加值系統

(18.204.56.185) 您好!臺灣時間:2022/08/17 15:54
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:謝富順
研究生(外文):Fu-Shuen Shie
論文名稱:一般化的分數單根分配
論文名稱(外文):Generalized Fractional Unit Root Distribution
指導教授:楊筑安楊筑安引用關係李慶男李慶男引用關係
指導教授(外文):Ju-Ann YangChingnun Lee
學位類別:碩士
校院名稱:國立高雄第一科技大學
系所名稱:金融營運所
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:31
中文關鍵詞:自我迴歸移動平均分數整合模型分數單根分配蒙地卡羅模擬單根檢定分數布朗運動
外文關鍵詞:Monte Carlo SimulationARFIMA modelfractional Brownian motionfractional unit root distributionunit root test
相關次數:
  • 被引用被引用:1
  • 點閱點閱:266
  • 評分評分:
  • 下載下載:50
  • 收藏至我的研究室書目清單書目收藏:0
摘要

在本文中,我們首先推導出一個ARFIMA(p, d, q)序列其部份和(partial sums)的漸近理論。然後我們研究一個AR(1)模型其干擾項在ARIFMA(p, d, q)的假設下去觀察斜率項OLS估計式的漸近行為。當分數差分參數d>0時,此分配會與Sowell (1990)所推導的結果相同,Sowell (1990)對干擾項的假設是為ARFIMA(0, d, 0);但是當 d<0時,則ARMA項將會影響漸近分配。

在引用參數化的條件下,我們推導出一個ARFIMA(p, d, q)序列的函數極限定理並且這樣的推導正好與其他學者在非參數化的表達法下所推導出來的結果相同,例如,Davidson and De Jong (2000)和Chung (2002)。我們發現,當d>0時,一般化的分數單根分配其極限分配與Sowell (1990)的結果一樣,但是當d<0時,則ARMA項將有助於決定此極限分配。

最後,由蒙地卡羅模擬的結果可知,當一時間序列包含ARMA項時,則將決定Dickey-Fuller檢定的檢定力。
ABSTRACT
In this paper, we first develop an asymptotic theory for the partial sums of an ARFIMA(p,d,q) process. Then we study the asymptotic behavior of OLS slope estimator under a AR(1) model with an ARFIMA(p,d,q) error. When the fractional difference parameter d>0, this distribution converge to the same one with Sowell (1990) where error is assumed to be ARFIMA(0,d,0). While in the situation d<0, the ARMA component in the error process help to determine the asymptotic distribution.
The conditions we imposed to derive the functional limit theorem for an ARFIMA(p, d, q) process are parametric and they are shown to be appropriate as alternative interpretation of the same results from nonparametric conditions imposed by other authors, such as Davidson and De Jong (2000) and Chung (2002). Our findings are when d>0, the limiting distribution of the generalized fractional unit root are the same with the results of Sowell (1990) in the corresponding d. However, in the case when d<0, the ARMA component help to determine this limiting distribution.
Finally, by the Monte Carlo results indicate that ARMA component determine the power of Dickey-Fuller test.
目錄
頁次
中文提要i
英文提要ii
誌謝iii
目錄iv
表目錄vi
第一章 緒論 1
第一節 研究動機與目的 1
第二節 研究架構 2
第二章 文獻回顧與探討 3
第一節 Dickey-Fuller(D-F)單根檢定 4
第二節 Augmented Dickey-Fuller(ADF)單根檢定 5
第三節 Phillips-Perron(P-P)單根檢定 6
第四節 Sowell 分數單根分配 8
第三章 預備的觀念 10
第一節 自我迴歸移動平均分數整合(ARFIMA)模型10
第二節 分數布朗運動 13
第四章 ARFIMA序列的單根分配及蒙地卡羅模擬 17
第一節 自我迴歸移動平均分數整合序列的單根分配17
第二節 蒙地卡羅模擬 20
第五章 結論 23
附錄 24
參考文獻 30

表目錄
表1 不同的ARFIMA(p, d, q)模型下其拒絕虛無假設的百分比21
表2 AR與MA項之係數值的變化對檢定力的影響 22
參考文獻(1)Avram, F. and M. S. Taqqu (1987) “Noncentral Limit Theorems and Appell Polynomials,” Annals of Probability, 15, 767-775.(2)Baillie, R. T. (1996) “Long Memory Processes and Fractional Integration in Econometrics,” Journal of Econometrics, 73, 5-59.(3)Chan, N. H. and T. Norma (1995) “Inference for Unstable Long-Memory Processes with Applications to Fractional Unit Root Autoregressions,” The Annals of Statistics, Vol. 23, No. 5, 1662-1683.(4)Chung, C. F. (2002) “Sample Means, Sample Autocovariances, and Linear Regression of Stationary Multivariate Long Memory Processes,” Econometric Theory, 18, 51-78.(5)Davidson, J. and R. M. De Jong (2000) “The Functional Central Limit Theorem and Weak Convergence to Stochastic Integrals II” Econometric Theory, 16, 643-666.(6)Davydov, Y. A. (1970) “The Invariance Principle for Stationary Processes, “ Theory of Probability and Its Applications, 15, 487-489.(7)Dicky, D. A. and W. A. Fuller (1979) “Distribution of the Estimator for Autoregressive Time Series with a Unit Root,“ Journal of the American Statistical Association, 74, 427-431.(8)Dicky, D. A. and W. A. Fuller (1981) “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root,” Econometrica, 49, 1057-1072.(9)Diebold, F. X. and G. D. Rudebusch (1991) “On the power of Dickey-Fuller tests against fractional alternatives,” Economics Letters, 35, 155-160.(10)Ellis, C. (1999) “Estimation of the ARFIMA(p, d, q) Fractional Differencing Parameter (d) Using the Classical Rescaled Adjusted Range Technique,” International Review of Financial Analysis, 8:1, 53-65.(11)Geweke, J. F. and S. P. Hudak (1983) “The Estimation and Application of Long Memory Time Series Models,” Journal of Time Series Analysis, 4, 221-238.(12)Granger, C. W. J. (1980) “Long Memory Relationships and the Aggregation of Dynamic Models,” Journal of Econometrics, 14, 227-238.(13)Granger, C. W. J. (1981) “Some Properties of Time Series Data and Their Use in Econometric Model Specification,” Journal of Econometrics, 16, 121-130.(14)Granger, C. W. J. and R. Joyeux (1980) “An Introduction to Long-Memory Time Series Models and Fractional Differencing,” Journal of Time Series Analysis, 1, 15-29.(15)Hassler, U. and J. Wolters (1994) “On the Power of unit root tests against fractional alternatives,” Economics Letters, 45, 1-5.(16)Hosking, J. R. M. (1981) “Fractional differencing,” Biometrika, 68, 1, 165-176.(17)Marinucci, D. and P. M. Robinson (1999) “Alternative forms of Fractional Brownian Motion,” Journal of Statistical Planning and Inference, 80, 111-122.(18)Mandelbrot, B. B. and J. W. Van Ness (1968) “Fractional Brownian Motions, Fractional Brownian noises and applications,” SIAM Review, 10, 422-437.(19)Phillips, P. C. B. and P. Perron (1988) “Testing for Cointegration using Principle Components Methods,” Journal of Economic Dynamics and Control, 12, 205-230.(20)Phillips, P. C. B. (1987) “Time Series Regression with a Unit Root,” Econometrica, Vol. 55, 277-301.(21)Sowell, F. B. (1990) “The Fractional Unit Root Distribution,” Econometrica, Vol. 58, No. 2, 495-505.(22)Sowell, F. B. (1992a) “Maximum Likelihood Estimation of Stationary Univarite Fractionally Integrated Time Series Models,” Journal of Econometrics, 53, 165-188.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top