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研究生:王詩瑋
研究生(外文):WANG, SHIH-WEI
論文名稱:對分數性整合過程之非線性轉換的研究-以蒙地卡羅方法
論文名稱(外文):NONLINEAR TRANSFORMATIONS OFFRACTIONAL INTEGRATED TIME SERIES-BY MONTE-CARLO SIMULATIONSNonlinear Transformations of Fractional Integrated Time Series-by Monte-Carlo Simulations
指導教授:王健合
指導教授(外文):WANG, CHIEN-HO
學位類別:碩士
校院名稱:國立臺北大學
系所名稱:經濟學系
學門:社會及行為科學學門
學類:經濟學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:44
中文關鍵詞:分數性整合過程非線性轉換
外文關鍵詞:Fractional Integrated processesNonlinear Transformations
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本文主要研究的是非線性轉換對分數性整合過程的影響,將實證資料作非線性轉換是計量上常見的方法,但卻會造成資料性質的扭曲,所以便產生了採取非線性轉換是否適宜的問題,如果藉由傳統的DF與ADF單根檢定能正確判別出轉換後數列與原數列的異同,就能得知轉換是否會產生扭曲。

模擬的結果如下:x2、x3和|x|轉換的相關係數衰退速度較原數列略快,表示這三種轉換扭曲的程度較小,但其檢定力偏低,表示單根檢定不易正確區別出數列性質已改變,此外,檢定力與d值呈負相關;sin(x)轉換會大幅增加數列衰退速度,幾乎使數列變成穩定狀態,單根檢定具有相當高的檢定力,表示能正確判別轉換後數列性質已改變;exp(x)與ln |x|轉換也會使數列衰退速度略為下降,但其單根檢力維持較高的水準,且會隨d值增加而增加;ln(x+75)與1/(x+75)轉換不會改變數列衰退速度,新數列的性質與原數列一樣,其檢定顯著水準不受轉換影響;而在面對相同轉換時,DF的檢定力均較ADF高,但不論是DF或ADF的檢定力都會隨觀察值個數的增加而增加,表示兩者皆具有檢定上的一致性。

當待檢測數列的性質與基準數列的性質越相似,就越容易產生低檢力的問題。但因非線性轉換對於數列的扭曲程度較難分解,而影響檢定力的原因也很多,所以本文僅能以可觀察到的現象來解釋影響檢定力的原因,例如:非線性轉換對於數列扭曲的程度,可藉由相關係數的衰退程度大略判斷出來,對於實驗性分配的影響,則可由分配的位移或擴散程度來看,其中實驗性分配的變動也可以用來解釋檢定力低的原因。
We investigate the effect of nonlinear transformations on fractional integrated process and unit root tests with Monte-Carlo methods. Nonlinear transformations may change the original characteristics of I(d) process. Economists may misjudge the true series with transformed time series. In this thesis, we consider three directions to research the characteristics of transformed I(d) process: autocorrelations, Dicky-Fuller unit root tests and Phillips-Ouliaris cointegration tests.

According to simulations, we find following results. First, x2, x3 and |x| increase the rate of decay slowly, however, the powers of tests are quite low and decrease with d. sin(x) makes series become stationary and has highest power. exp(x) and ln |x| increase the rate of decay. When d increases, the test powers of exp(x) and ln |x| are higher than x2, x3 and |x|. ln(x+75) and 1/(x+75) do not make series difference and keep originally significanced values. Second, for fixed d, power of DF tests for transformed series are higher than power of ADF tests. Third, for fixed d and transformation, powers increase with sample size which means DF and ADF tests are consistent.

When the transformed series are similar with original I(d) series, using unit root tests distinguish I(d) series with transformed series hardly. There are many reasons which cause powers have different direction with d increase. By simulations, I find autocorrlations and empirical distributions can explain this phenomena.
目 錄
第一章 緒論 1
第一節 研究動機與目的 1
第二節 研究架構 3
第二章 文獻回顧 4
第一節 傳統檢定V.S I(d)過程 4
第二節 傳統檢定V.S非線性轉換 6
第三章 研究方法 8
第一節 分數性整合過程之簡介 8
第二節 研究方法 10
一、Dickey-Fuller單根檢定(DF) 10
二、Augment Dickey-Fuller單根檢定(ADF) 12
三、分數性單根檢定 13
第三節 模擬步驟與設定 15
第四章 模擬結果 19
第一節 判斷 19
第二節 DF單根檢定之模擬結果 21
第三節 ADF單根檢定之模擬結果 23
第四節 分析結果 24
第五章 分數共整合檢定 26
第一節 分數共整合簡介 26
第二節 模擬與檢定過程 27
第三節 檢定結果 28
第六章 結論與建議 30
第一節 總結 30
第二節 研究限制與建議 31
參考文獻 32
附錄一 落後1~10期相關係數(T=2000) 34
附錄二 DF檢定臨界值(N=2000) 36
附錄三 ADF檢定臨界值(N=2000) 40
附錄四 模擬I(d)過程之程式(GAUSS 6.0) 44
參考文獻

謝富順(2001),《一般化的分數單根分配》,國立高雄第一科技大學金融營運所碩士論文。

Baillie, Richard T. (1996),“Long Memory Processes and Fractional Integration in Econometrics,”Journal of Econometrics, 73, 5-59.

Dickey, D.A. and W.A. Fuller (1979), “Distribution of the Estimators for Autoregressive Time Series with a Unit Root, ” Journal of American Statistical Association, 74, 427-431.

Diebold, Francis X. and Glen D. Rudebusch (1991),“On the Power of Dicky-Fuller Tests against Fractional Alternatives,”Economics Letters, 35, 115-160.

Dittmann, Ingolf and C. W. J. Granger (2002), “Properties of Nonlinear Transformations of Fractional Integrated Processes, ” Journal of Econometrics, 110, 113-133.

Dolado, Juan J. , Jesús Gonzalo and Laura Mayoral (2002), “A Fractional Dicky-Fuller Test for Unit Roots, ” Econometrics, 70:5, 1963-2006.

Engle, R.F. and C.W.J. Granger (1987), “Cointegration and Error Correction: Representation, Estimation, and Testing, ” Econometrica, 55, 251-276.

Granger, C.W.J. (1981), “Some Properties of Time Series Data and Their Use in Econometric Model Specification, ” Journal of Econometrics, 16, 121-130.

Granger, C.W.J. (1986), “Developments in the Study of Cointegrated EconomicVariables, ” Oxford Bulletin of Economics and Statistics, 48, 213-228.

Granger, C. W. J. and Jeff Hallman (1991),“Nonlinear Transformations of Integrated Time Series,”Journal of Time Series Analysis, 12:3, 207-218.

Hamilton, James D. (1994), Time Series Analysis, Princeton, New Jersey, Princeton University Press.

Hassler, Uwe and Jürgen Wolters (1994), “On the Power of Unit Root Tests against Fractional Alternatives, ”Economics Letters, 45, 1-5.

Krämer, Walter (1998), “Fractional Integration and the Augmented Dicky-Fuller Test, ” Economics Letters, 61, 269-272.

Lee, Chingnun, Chien-Min Chuang and Fu-Shuen Shie (2003),“On the Power of the Augmented Dickey-Fuller Test of Unit Root against Fractionally-Integrated Alternatives, ” Working paper, Graduate Institution of Economics, National Sun Yat-sen University.

Lee Chingnun and Fu-Shuen Shie (2004),“Fractional Integration and the Phillips-Perron Test,”Academia Economic Papers, 32:2, 273-312.

Park, J. Y. and P. C. B. Phillips (1999), “Asymptotic for nonlinear transformations of integrated time series, ” Econometric Theory, 15, 269-298.

Phillips, P.C.B and S. Ouliaris (1990). “Asymptotic Properties of Residual Based Tests for Cointegration, ” Econometrica, 58, 165-193.

Phillips, P.C.B. and P. Perron (1988), “Testing for a Unit Root in Time Series Regression, ” Biometrika, 75, 335-346.

Said, S.E. and D.A. Dickey (1984), “Testing for Unit Root in Autoregressive Moving Average Models of Unknown Order, ” Biometrika, 71, 599-608.

Sowell, Fallaw (1990),“The Fractional Unit Root Distribution,”Econometrica, 58: 2, 495-505.

Tyurin, K. and P. C. B. Phillips (1999), “The occupation density of fractional Brownian motion and some of its applications, ” Working paper, Department of Economics, Yale University.
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