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題名 自我迴歸模型的動差估計與推論
Estimation and inference in autoregressive models with method of moments作者 陳致綱
Chen, Jhih Gang貢獻者 郭炳伸
Kuo, Biing Shen
陳致綱
Chen, Jhih Gang關鍵詞 差分模型
動差法
自我迴歸模型
追蹤資料模型
固定效果
單根檢定
difference model
method of moments
autoregressive model
panel data model
fixed effects
unit root test日期 2009 上傳時間 9-May-2016 14:53:34 (UTC+8) 摘要 本論文的研究主軸圍繞於自我迴歸模型的估計與推論上。文獻上自我迴歸模型的估計多直接採用最小平方法, 但此估計方式卻有兩個缺點:(一)當序列具單根時,最小平方估計式的漸近分配為非正規型態,因此檢定時需透過電腦模擬得到臨界值;(二)最小平方估計式雖具一致性,但卻有嚴重的有限樣本偏誤問題。有鑑於此,我們提出一種「二階差分轉換估計式」,並證明該估計式的偏誤遠低於前述最小平方估計式,且在序列為粧定與具單根的環境下具有相同的漸近常態分配。此外,二階差分轉換估計式相當適合應用於固定效果追蹤資料模型,而據以形成的追蹤資料單根檢定在序列較短的情況下仍有不錯的檢定力。 本論文共分四章,茲分別簡單說明如下: 第1章為緒論,回顧文獻上估計與推論自我回歸模型時的問題,並說明本論文的研究目標。估計自我迴歸模型的傳統方式是直接採取最小平方法,但在序列具單根的情況下由於訊息不隨時間消逝而快速累積,使估計式的收斂速度高於序列為恒定的情況。不過,這也導致最小平方估計式的漸近分配為非標準型態,並使得進行假設檢定前必須先透過電腦模擬來獲得臨界值。其次,最小平方估計式雖具一致性,但在有限樣本下卻是偏誤的。實證上, 樣本點不多是研究者時常面臨的窘境,並使得小樣本偏誤程度格外嚴重。本章中透過對前述問題形成因素的瞭解,說明解決與改善的方法,亦即我們提出的「二階差分轉換估計式」。 第2章主要目的在於推導二階差分轉換估計式之有限樣本偏誤。我們亦推導了多階差分自我迴歸模型下二階段最小平方估計式(two stage least squares, 2SLS)與 Phillips andHan (2008)採用的一階差分轉換估計式之偏誤,以同時進行比較。本章理論與模擬結果皆顯示,一階與二階差分轉換估許式與2SLS之 $T^{−1}$ 階偏誤程度皆低於以最小平方法估計原始準模型(level model)的偏誤,其中 T 為時間序列長度。另外,一階差分轉換估計式與二階差分轉換估計式在 $T^{−1}$ 階偏誤上,分別與一階和二階差分模型下2SLS相同,但兩估計式的相對偏誤程度則因自我相關係數的大小而互有優劣。同時,我們發現估計高於二階的差分模型對小樣本偏誤並無法有更進一步的改善。最後,即使在樣本點不多的情況下,本章所推導的偏誤理論對於實際偏誤仍有良好的近似能力。 第3章主要目的在於發展二階差分轉換估計式之漸近理論。與 Phillips and Han (2008) 採用之一階差分轉換估計式相似的是,該估計式在序列為恒定與具單根的情況下收斂速度相同,並有漸近常態分配的優點。值得注意的是, 二階差分轉換估計式的漸近分配為 N(0,2),不受任何未知參數的影響。另外,當序列呈現正自我相關時,二階差分轉換估計式相較於一階差分轉換估計式具有較小的漸近變異數,進而使得據以形成的檢定統計量有較佳的對立假設偵測能力。最後, 誠如 Phillips and Han (2008) 所述,由於差分過程消除了模型中的截距項,使得此類估計方法在固定效果的動態追蹤資料模型(dynamic panel data model with fixed effect) 具相當的發展與應用價值。 本論文第4 章進一步將二階差分轉換估計式推展至固定效果的動態追蹤資料模型。文獻上估計此種模型通常利用差分來消除固定效果後,再以一般動差法 (generalized method of moments, GMM) 進行估計。然而,這樣的估計方式在序列為近單根或具單根時卻面臨了弱工具變數(weak instrument)的問題,並導致嚴重的估計偏誤。相反的,差分轉換估計式所利用的動差條件在近單根與單根的情況下仍然穩固,因此在小樣本下的估計偏誤相當輕微(甚至無偏誤)。另外,我們證明了不論序列長度(T )或橫斷面規模(n)趨近無窮大,差分轉換估計式皆有漸近常態分配的性質。與單一序列時相同的是,我們提出的二階差分轉換估計式在序列具正自我相關性時的漸近變異數較一階差分轉換估計式小;受惠於此,利用二階差分轉換估計式所建構的檢定具有較佳的檢力。值得注意的是,由於二階差分轉換估計式在單根的情況下仍有漸近常態分配的性質,我們得以直接利用該漸近理論建構追蹤資料單根檢定。電腦模擬結果發現,在小 T 大 n 的情況下,其檢力優於文獻上常用的 IPS 檢定(Im et al., 1997, 2003)。
This thesis deals with estimation and inference in autoregressive models. Conventionally, the autoregressive models estimated by the least squares (LS) procedure may be subject to two shortcomings. First, the asymptotic distribution of the LS estimates for autoregressive coefficient is discontinuous at unity. Test statistics based on the LS estimates thus follow nonstandard distributions, and the critical values obtained need to rely on Monte Carlo techniques. Secondly, as is well known, the LS estimates of autoregressive models are biased in finite samples. This bias could be substantial and leads to serious size distortion for the test statistics built on the estimates and forecast errors. In this thesis,we consider a simple newmethod ofmoments estimator, termed the “transformed second-difference” (hereafter TSD) estimator, that is without the aforementioned problems, and has many useful applications. Notably, when applied to dynamic panel models, the associated panel unit root tests shares a great power advantage over the existing ones, for the cases with very short time span. The thesis consists of 4 chapters, which are briefly described as follows. 1. Introduction: Overview and Purpose This chapter first reviews the literature and states the purpose of this dissertation. We discuss the sources of problems in estimating autoregressive models with the conventional method. The motivation to estimate the autoregressive series with multiple-difference models, instead of the conventional level model, is provided. We then propose a new estimator, the TSD estimator, which can avoid (fully or partly) the drawbacks of the LS method, and highlight its finite-sample and asymptotic properties. 2. The Bias of 2SLSs and transformed difference estimators in Multiple-Difference AR(1) Models In this chapter, we derive approximate bias for the TSD estimator. For comparisons, the corresponding bias of the two stage least squares estimators (2SLS) in multiple-difference AR(1) models and the transformed first-difference (TFD) estimator proposed by Chowdhurry (1987) are also given as by-products. We find that: (i) All the estimators considered are much less biased than the LS ones with the level regression; (ii)The difference method can be exploited to reduce the bias only up to the order of difference 2; and (iii) The bias of the TFD and TSD estimators share the same order at $O(T^{-1})$ as that of 2SLSs. However, to the extent of bias reductions, neither the 2 considered transformed difference estimators shows a uniform dominance over the entire parameter space. Our simulation evidence lends credible supports to our bias approximation theory. 3. Gaussian Inference in AR(1) Time Series with or without a Unit Root The goal of the chapter is to develop an asymptotic theory of the TSD estimator. Similar to that of the TFD estimator shown by Phillips and Han (2008), the TSDestimator is found to have Gaussian asymptotics for all values of ρ ∈ (−1, 1] with $\\sqrt{T}$ rate of convergence, where ρ is the autoregressive coefficient of interest and T is the time span. Specifically, the limit distribution of the TSD estimator is N(0,2) for all possible values of ρ. In addition, the asymptotic variance of the TSD estimator is smaller than that of the TFD estimator for the cases with ρ > 0, and the corresponding t -test thus exhibits superior power to the TFD-based one. 4. Estimation and Inference with Moment Methods for Dynamic Panels with Fixed Effects This chapter demonstrates the usefulness of the TSD estimator when applying to to dynamic panel datamodels. We find again that the TSD estimator displays a standard Gaussian limit, with a convergence rate of $\\sqrt{nT}$ for all values of ρ, including unity, irrespective of how n or T approaches infinity. Particularly, the TSD estimator makes use of moment conditions that are strong for all values of ρ, and therefore can completely avoid the weak instrument problem for ρ in the vicinity of unity, and has virtually no finite sample bias. As in the time series case, the asymptotic variance of the TSD estimator is smaller than that of the TFD estimator of Han and Phillips (2009) when ρ > 0 and T > 3, and the corresponding t -ratio test is thus more capable of unveiling the true data generating process. Furthermore, the asymptotic theory can be applied directly to panel unit root test. Our simulation results reveal that the TSD-based unit root test is more powerful than the widely used IPS test (Im et al, 1997, 2003) when n is large and T is small.參考文獻 1. Alonso-Borrego, C. and M. Arellano (1999), “Symmetrically Normalized Instrumental-Variable Estimation Using Panel Data,” Journal of Business & Economic Statistics, 17, 36−49. 2. Anderson, T.W. and C. Hsiao (1981), “Estimation of Dynamic Models with Error Components,” Journal of American Statistical Association, 76, 598−606. 3. Anderson, T.W. and C. Hsiao (1982), “Formulation and Estimation of Dynamic Models Using Panel Data,” Journal of Econometrics, 18, 47−82. 4. Arellano, M. and S.R. Bond (1991), “Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations,” Review of Economic Studies, 58(2), 277−297. 5. Bartlett,M.S. (1946), “On the Theoretical Specification and Sampling properties of Autocorrelated Time Series,” Supplement to the Journal of the Royal Statistical Society, 8, 27−41. 6. Blundell, R. and S. Bond (1998), “Initial Conditions and Moment Restrictions in Dynamic Panel Data Models,” Journal of Econometrics, 87(1), 115−143. 7. Breitung, J. (2000), “The Local Power of Some Unit Root Tests for Panel Data,” in: B. Baltagi (ed.), Nonstationary Panels, Panel Cointegration, and Dynamic Panels, Advances in Econometrics, Vol. 15, JAI: Amsterdam, 161-178. 8. Bun,M.J.G. andM.A. Carree (2006), “Bias-Corrected Estimation in Dynamic Panel Data Models,” Journal of Business and Economic Statistics, 23(2), 200−210. 9. Chowdhury, G. (1987), “A Note on Correcting Biases in Dynamic Panel Models,” Applied Economics, 19, 31−37. 10. Hahn, J., J. Hausman, and G. Kuersteiner (2007), “Long Difference Instrumental Variables Estimation for Dynamic Panel Models with Fixed Effects,” Journal of Econometrics, 140(2), 574−617. 11. Hahn, J. and G. Kuersteiner (2002), “Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects When Both n and T are Large,” Econometrica, 70, 1639−1657. 12. Han, C. and P.C.B. Phillips (2009), “GMM Estimation for Dynamic Panels with Fixed Effects and Strong Instruments at Unity," Econometric Theory, forthcomming. 13. Hansen, B. (2007), “Least Squares Model Averaging,” Econometrica, 75(4), 1175−1189. 14. Hayakawa, K. (2006), “A Note on Bias in First-Differenced AR(1) Models,” Economics Bulletin, 3(27), 1−10. 15. Im, K.S., M. H. Pesaran, and Y. Shin (1997), “Testing for Unit Roots in Heterogeneous Panels,”Working paper, University of Cambridge. 16. Im, K.S., M.H. Pesaran, and Y. Shin (2003), “Testing for Unit Roots in Heterogeneous Panels,” Journal of Econometrics, 115, 53−74. 17. Judge G. G. and R.Mittelhammer (2004), “A Semiparametric Basis for Combing Estimation Problems under Quadratic Loss,” Journal of American Statistical Association, 99, 479−487. 18. Kendall, M.G. (1954), “Note on the Bias in the Estimation of Autocorrelation,” Biometrika, 41, 403−404. 19. Kilian, L. (1998), “Confidence Intervals for Impulse Responses Under Departures from Normality,” Econometric Reviews, 17(1), 1−29. 20. Kim, Jae H (2001), “Bootstrap-after-Bootstrap Prediction Intervals for Autoregressive Models,” Journal of Business and Economic Statistics, 19(1), 117−128. 21. Kiviet, J.F. (1995), “On Bias, Inconsistency, and Efficiency of Various Estimators in Dynamic Panel DataModels,” Journal of Econometrics, 68, 53−78. 22. Kuo, B.S. and W.J. Tsay (2008), “Averaging Estimator by Combining Multiple Differencing and Long-Distance Differencing Operators,” Working Paper. 23. Levin, A., C.F. Lin and C.S. Chu (2002), “Unit Root Test in Panel Data: Asymptotic and Finite Sample Properties,” Journal of Econometrics, 108, 1−24. 24. MacKinnon, J.G. and A.A. Smith, Jr. (1998), “Approximate Bias Correction in Econometrics,” Journal of Econometrics, 85, 205−230. 25. Marriott, F.H.C. and J.A. Pope (1954), “Bias in the Estimation of Autocorrelations,” Biometrika, 41, 393−402. 26. Moon, H.R., B. Perron, and P.C.B. Phillips (2007), “Incidental Trends and the Power of Panel Unit Root Tests,” Journal of Econometrics, 141, 416−459. 27. Orcutt, G.H. (1948) “A Study of the Autoregressive Nature of the Times Series Used for Tinbergen’s Model of the Economic System of the United States,” Journal of the Royal Statistical Society, Series B, 1−45. 28. Patterson, K.D. (2000), “Bias Reduction in Autoregressive Models,” Economics Letters, 68, 135−142. 29. Phillips, P.C.B. (1977), “Approximations to Some Finite Sample Distributions Associated with a First Order Stochastic Difference Equation,” Econometrica, 45, 463−485. 30. Phillips, P.C.B. andC.Han (2008), “Gaussian Inference in AR(1) Time Series with orwithout a Unit Root,” Econometric Theory, 24, 631−650. 31. Phillips, P.C.B. and V. Solo (1992), “Asymptotics for Linear Processes," The Annals of Statistics, 20(2), 971−1001. 32. Phillips, P.C.B. and D. Sul (2007), “Bias in Dynamic Panel Estimation with Fixed Effects, Incidental Trends and Cross Section Dependence,” Journal of Econometrics, 137(1), 162−188. 33. Shaman, P. and R.A. Stine (1988), “The Bias of Autoregressive Coefficient Estimators,” Journal of American Statistical Association, 83, 842−848. 34. Shaman, P. and R.A. Stine (1989), “A Fixed Point Characterization for Bias of Autoregressive Estimators,” The Annals of Statistics, 17, 1275−1284. 35. Tanaka, K. (1984), “An Asymptotic Expansion Associated with theMaximum Likelihood Estimators in ARMAModels,” Journal of the Royal Statistical Society, Ser. B, 46, 58−67. 36. Tanizaki, H. (2000), “Bias Correction of OLSE in the Regression Model with Lagged Dependent Variables,” Computational Statistics and Data Analysis, 34(4), 495−511. 37. Tanizaki, H., S. Hamori and Y. Matsubayashi (2006), “On Least-Squares Bias in the AR(p) Models: Bias Correction Using the Bootstrap Methods,” Statistical Papers, 47(1), 109−124. 38. White,H. (1984), Asymptotic Theory for Econometricians,Orlando, Fla.: Academic Press. 描述 博士
國立政治大學
國際經營與貿易學系
90351502資料來源 http://thesis.lib.nccu.edu.tw/record/#G0903515021 資料類型 thesis dc.contributor.advisor 郭炳伸 zh_TW dc.contributor.advisor Kuo, Biing Shen en_US dc.contributor.author (Authors) 陳致綱 zh_TW dc.contributor.author (Authors) Chen, Jhih Gang en_US dc.creator (作者) 陳致綱 zh_TW dc.creator (作者) Chen, Jhih Gang en_US dc.date (日期) 2009 en_US dc.date.accessioned 9-May-2016 14:53:34 (UTC+8) - dc.date.available 9-May-2016 14:53:34 (UTC+8) - dc.date.issued (上傳時間) 9-May-2016 14:53:34 (UTC+8) - dc.identifier (Other Identifiers) G0903515021 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/95070 - dc.description (描述) 博士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 國際經營與貿易學系 zh_TW dc.description (描述) 90351502 zh_TW dc.description.abstract (摘要) 本論文的研究主軸圍繞於自我迴歸模型的估計與推論上。文獻上自我迴歸模型的估計多直接採用最小平方法, 但此估計方式卻有兩個缺點:(一)當序列具單根時,最小平方估計式的漸近分配為非正規型態,因此檢定時需透過電腦模擬得到臨界值;(二)最小平方估計式雖具一致性,但卻有嚴重的有限樣本偏誤問題。有鑑於此,我們提出一種「二階差分轉換估計式」,並證明該估計式的偏誤遠低於前述最小平方估計式,且在序列為粧定與具單根的環境下具有相同的漸近常態分配。此外,二階差分轉換估計式相當適合應用於固定效果追蹤資料模型,而據以形成的追蹤資料單根檢定在序列較短的情況下仍有不錯的檢定力。 本論文共分四章,茲分別簡單說明如下: 第1章為緒論,回顧文獻上估計與推論自我回歸模型時的問題,並說明本論文的研究目標。估計自我迴歸模型的傳統方式是直接採取最小平方法,但在序列具單根的情況下由於訊息不隨時間消逝而快速累積,使估計式的收斂速度高於序列為恒定的情況。不過,這也導致最小平方估計式的漸近分配為非標準型態,並使得進行假設檢定前必須先透過電腦模擬來獲得臨界值。其次,最小平方估計式雖具一致性,但在有限樣本下卻是偏誤的。實證上, 樣本點不多是研究者時常面臨的窘境,並使得小樣本偏誤程度格外嚴重。本章中透過對前述問題形成因素的瞭解,說明解決與改善的方法,亦即我們提出的「二階差分轉換估計式」。 第2章主要目的在於推導二階差分轉換估計式之有限樣本偏誤。我們亦推導了多階差分自我迴歸模型下二階段最小平方估計式(two stage least squares, 2SLS)與 Phillips andHan (2008)採用的一階差分轉換估計式之偏誤,以同時進行比較。本章理論與模擬結果皆顯示,一階與二階差分轉換估許式與2SLS之 $T^{−1}$ 階偏誤程度皆低於以最小平方法估計原始準模型(level model)的偏誤,其中 T 為時間序列長度。另外,一階差分轉換估計式與二階差分轉換估計式在 $T^{−1}$ 階偏誤上,分別與一階和二階差分模型下2SLS相同,但兩估計式的相對偏誤程度則因自我相關係數的大小而互有優劣。同時,我們發現估計高於二階的差分模型對小樣本偏誤並無法有更進一步的改善。最後,即使在樣本點不多的情況下,本章所推導的偏誤理論對於實際偏誤仍有良好的近似能力。 第3章主要目的在於發展二階差分轉換估計式之漸近理論。與 Phillips and Han (2008) 採用之一階差分轉換估計式相似的是,該估計式在序列為恒定與具單根的情況下收斂速度相同,並有漸近常態分配的優點。值得注意的是, 二階差分轉換估計式的漸近分配為 N(0,2),不受任何未知參數的影響。另外,當序列呈現正自我相關時,二階差分轉換估計式相較於一階差分轉換估計式具有較小的漸近變異數,進而使得據以形成的檢定統計量有較佳的對立假設偵測能力。最後, 誠如 Phillips and Han (2008) 所述,由於差分過程消除了模型中的截距項,使得此類估計方法在固定效果的動態追蹤資料模型(dynamic panel data model with fixed effect) 具相當的發展與應用價值。 本論文第4 章進一步將二階差分轉換估計式推展至固定效果的動態追蹤資料模型。文獻上估計此種模型通常利用差分來消除固定效果後,再以一般動差法 (generalized method of moments, GMM) 進行估計。然而,這樣的估計方式在序列為近單根或具單根時卻面臨了弱工具變數(weak instrument)的問題,並導致嚴重的估計偏誤。相反的,差分轉換估計式所利用的動差條件在近單根與單根的情況下仍然穩固,因此在小樣本下的估計偏誤相當輕微(甚至無偏誤)。另外,我們證明了不論序列長度(T )或橫斷面規模(n)趨近無窮大,差分轉換估計式皆有漸近常態分配的性質。與單一序列時相同的是,我們提出的二階差分轉換估計式在序列具正自我相關性時的漸近變異數較一階差分轉換估計式小;受惠於此,利用二階差分轉換估計式所建構的檢定具有較佳的檢力。值得注意的是,由於二階差分轉換估計式在單根的情況下仍有漸近常態分配的性質,我們得以直接利用該漸近理論建構追蹤資料單根檢定。電腦模擬結果發現,在小 T 大 n 的情況下,其檢力優於文獻上常用的 IPS 檢定(Im et al., 1997, 2003)。 zh_TW dc.description.abstract (摘要) This thesis deals with estimation and inference in autoregressive models. Conventionally, the autoregressive models estimated by the least squares (LS) procedure may be subject to two shortcomings. First, the asymptotic distribution of the LS estimates for autoregressive coefficient is discontinuous at unity. Test statistics based on the LS estimates thus follow nonstandard distributions, and the critical values obtained need to rely on Monte Carlo techniques. Secondly, as is well known, the LS estimates of autoregressive models are biased in finite samples. This bias could be substantial and leads to serious size distortion for the test statistics built on the estimates and forecast errors. In this thesis,we consider a simple newmethod ofmoments estimator, termed the “transformed second-difference” (hereafter TSD) estimator, that is without the aforementioned problems, and has many useful applications. Notably, when applied to dynamic panel models, the associated panel unit root tests shares a great power advantage over the existing ones, for the cases with very short time span. The thesis consists of 4 chapters, which are briefly described as follows. 1. Introduction: Overview and Purpose This chapter first reviews the literature and states the purpose of this dissertation. We discuss the sources of problems in estimating autoregressive models with the conventional method. The motivation to estimate the autoregressive series with multiple-difference models, instead of the conventional level model, is provided. We then propose a new estimator, the TSD estimator, which can avoid (fully or partly) the drawbacks of the LS method, and highlight its finite-sample and asymptotic properties. 2. The Bias of 2SLSs and transformed difference estimators in Multiple-Difference AR(1) Models In this chapter, we derive approximate bias for the TSD estimator. For comparisons, the corresponding bias of the two stage least squares estimators (2SLS) in multiple-difference AR(1) models and the transformed first-difference (TFD) estimator proposed by Chowdhurry (1987) are also given as by-products. We find that: (i) All the estimators considered are much less biased than the LS ones with the level regression; (ii)The difference method can be exploited to reduce the bias only up to the order of difference 2; and (iii) The bias of the TFD and TSD estimators share the same order at $O(T^{-1})$ as that of 2SLSs. However, to the extent of bias reductions, neither the 2 considered transformed difference estimators shows a uniform dominance over the entire parameter space. Our simulation evidence lends credible supports to our bias approximation theory. 3. Gaussian Inference in AR(1) Time Series with or without a Unit Root The goal of the chapter is to develop an asymptotic theory of the TSD estimator. Similar to that of the TFD estimator shown by Phillips and Han (2008), the TSDestimator is found to have Gaussian asymptotics for all values of ρ ∈ (−1, 1] with $\\sqrt{T}$ rate of convergence, where ρ is the autoregressive coefficient of interest and T is the time span. Specifically, the limit distribution of the TSD estimator is N(0,2) for all possible values of ρ. In addition, the asymptotic variance of the TSD estimator is smaller than that of the TFD estimator for the cases with ρ > 0, and the corresponding t -test thus exhibits superior power to the TFD-based one. 4. Estimation and Inference with Moment Methods for Dynamic Panels with Fixed Effects This chapter demonstrates the usefulness of the TSD estimator when applying to to dynamic panel datamodels. We find again that the TSD estimator displays a standard Gaussian limit, with a convergence rate of $\\sqrt{nT}$ for all values of ρ, including unity, irrespective of how n or T approaches infinity. Particularly, the TSD estimator makes use of moment conditions that are strong for all values of ρ, and therefore can completely avoid the weak instrument problem for ρ in the vicinity of unity, and has virtually no finite sample bias. As in the time series case, the asymptotic variance of the TSD estimator is smaller than that of the TFD estimator of Han and Phillips (2009) when ρ > 0 and T > 3, and the corresponding t -ratio test is thus more capable of unveiling the true data generating process. Furthermore, the asymptotic theory can be applied directly to panel unit root test. Our simulation results reveal that the TSD-based unit root test is more powerful than the widely used IPS test (Im et al, 1997, 2003) when n is large and T is small. en_US dc.description.tableofcontents 1 緒論---1 2 多階差分AR(1)模型下2SLS與差分轉換估計式之偏誤---5 2.1 前言----------5 2.2 多階差分模型、估計式與偏誤-----7 2.3 模擬-----------11 2.4 結論-----------14 3 恒定與具單根AR(1)序列之估計與推論-18 3.1 模型與回顧------------------18 3.2 二階差分轉換---------------19 3.3 時間趨勢模型--------------28 3.4 結論--------------------36 4 固定效果動態追蹤資料模型之估計與推論---------38 4.1 前言---------------------------------38 4.2 二階差分模型轉換與估計----------------40 4.3 時間趨勢模型------------------------48 4.4 追蹤資料單根檢定------------------55 4.5 結論------------------61 附錄-63 A 第2章理論證明---63 A.1 證明定理2.3 ---63 A.2 證明定理2.4 ----65 A.3 輔助定理5.1之推導---69 B 第3章理論證明-----71 B.1 證明定理3.1--------71 B.2 證明定理3.2---73 B.3 證明定理3.3-------------74 B.4 證明定理3.4 --------------74 C 第4章理論證明--------------76 C.1 證明定理4.1-------------76 C.2 證明定理4.2 ----------78 C.3 證明輔助定理4.3--------79 C.4 證明定理4.4 ---------80 C.5 證明定理4.5-------------81 參考文獻----------83 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0903515021 en_US dc.subject (關鍵詞) 差分模型 zh_TW dc.subject (關鍵詞) 動差法 zh_TW dc.subject (關鍵詞) 自我迴歸模型 zh_TW dc.subject (關鍵詞) 追蹤資料模型 zh_TW dc.subject (關鍵詞) 固定效果 zh_TW dc.subject (關鍵詞) 單根檢定 zh_TW dc.subject (關鍵詞) difference model en_US dc.subject (關鍵詞) method of moments en_US dc.subject (關鍵詞) autoregressive model en_US dc.subject (關鍵詞) panel data model en_US dc.subject (關鍵詞) fixed effects en_US dc.subject (關鍵詞) unit root test en_US dc.title (題名) 自我迴歸模型的動差估計與推論 zh_TW dc.title (題名) Estimation and inference in autoregressive models with method of moments en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 1. 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