| dc.contributor.advisor | 翁久幸 | zh_TW |
| dc.contributor.advisor | Weng, Chiu Hsing | en_US |
| dc.contributor.author (Authors) | 陳慎健 | zh_TW |
| dc.contributor.author (Authors) | Chen, Shen Chien | en_US |
| dc.creator (作者) | 陳慎健 | zh_TW |
| dc.creator (作者) | Chen, Shen Chien | en_US |
| dc.date (日期) | 2008 | en_US |
| dc.date.accessioned | 18-Sep-2009 20:11:16 (UTC+8) | - |
| dc.date.available | 18-Sep-2009 20:11:16 (UTC+8) | - |
| dc.date.issued (上傳時間) | 18-Sep-2009 20:11:16 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0913545031 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/36931 | - |
| dc.description (描述) | 博士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 統計研究所 | zh_TW |
| dc.description (描述) | 91354503 | zh_TW |
| dc.description (描述) | 97 | zh_TW |
| dc.description.abstract (摘要) | 本論文主要在估計門檻式自動迴歸模型之參數的信賴區間。由線性自動迴歸模型衍生出來的非線性自動迴歸模型中，門檻式自動迴歸模型是其中一種經常會被應用到的模型。雖然，門檻式自動迴歸模型之參數的漸近理論已經發展了許多；但是，相較於大樣本理論，有限樣本下參數的性質討論則較少。對於有限樣本的研究，Woodroofe (1989) 提出一種近似法：非常弱近似法。 Woodroofe 和 Coad (1997) 則利用此方法去架構一適性化線性模型之參數的修正信賴區間。Weng 和 Woodroofe (2006) 則將此近似法應用於線性自動迴歸模型。這個方法的應用始於定義一近似樞紐量，接著利用此方法找出近似樞紐量的近似期望值及近似變異數，並對此近似樞紐量標準化，則標準化後的樞紐量將近似於標準常態分配，因此得以架構參數的修正信賴區間。而在線性自動迴歸模型下，利用非常弱展開所導出的近似期望值及近似變異數僅會與一階動差及二階動差的微分有關。因此，本論文的研究目的就是在樣本數為適當的情況下，將線性自動迴歸模型的結果運用於門檻式自動迴歸模型。由於大部分門檻式自動迴歸模型的動差並無明確之形式；因此，本研究採用蒙地卡羅法及插分法去近似其動差及微分。最後，以第一階門檻式自動迴歸模型去配適美國的國內生產總值資料。 | zh_TW |
| dc.description.abstract (摘要) | Threshold autoregressive (TAR) models are popular nonlinear extension of the linear autoregressive (AR) models. Though many have developed the asymptotic theory for parameter estimates in the TAR models, there have been less studies about the finite sample properties. Woodroofe (1989) and Woodroofe and Coad (1997) developed a very weak approximation and used it to construct corrected confidence sets for parameters in an adaptive linear model. This approximation was further developed by Woodroofe and Coad (1999) and Weng and Woodroofe (2006), who derived the corrected confidence sets for parameters in the AR(p) models and other adaptive models. This approach starts with an approximate pivot, and employs the very weak expansions to determine the mean and variance corrections of the pivot. Then, the renormalized pivot is used to form corrected confidence sets. The correction terms have simple forms, and for AR(p) models it involves only the first two moments of the process and the derivatives of these moments. However, for TAR models the analytic forms for moments are known only in some cases when the autoregression function has special structures. The goal of this research is to extend the very weak method to the TAR models to form corrected confidence sets when sample size is moderate. We propose using the difference quotient method and Monte Carlo simulations to approximate the derivatives. Some simulation studies are provided to assess the accuracy of the method. Then, we apply the approach to a real U.S. GDP data. | en_US |
| dc.description.tableofcontents | Introduction 12 Preliminaries 3 2.1 Very weak approximations for AR(p) models 3 2.2 The Bootstrap method 6 2.2.1 non-parametric bootstrap 6 2.2.2 parametric bootstrap 73 The SETAR model with known threshold parameter 8 3.1 The SETAR model 8 3.2 Approximations 9 3.2.1 Approximation procedure 9 3.2.2 Error analysis 114 The SETAR model with unknown threshold parameter 17 4.1 Hansen`s approach 17 4.2 Smoothing approach 195 Experiments 25 5.1 Simulation 25 5.1.1 An AR(2) example 26 5.1.2 SETAR(2;1,1) examples with known threshold parameter 27 5.1.3 SETAR(2;1,1) examples with unknown threshold parameter 29 5.2 Real US GDP 306 Discussions 32 | zh_TW |
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| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0913545031 | en_US |
| dc.subject (關鍵詞) | 門檻式自動迴歸模型 | zh_TW |
| dc.subject (關鍵詞) | 非常弱近似法 | zh_TW |
| dc.subject (關鍵詞) | 適性化線性模型 | zh_TW |
| dc.subject (關鍵詞) | 修正信賴區間 | zh_TW |
| dc.subject (關鍵詞) | 蒙地卡羅法 | zh_TW |
| dc.subject (關鍵詞) | 差分法 | zh_TW |
| dc.subject (關鍵詞) | threshold autoregressive model | en_US |
| dc.subject (關鍵詞) | very weak approximation | en_US |
| dc.subject (關鍵詞) | adaptive linear model | en_US |
| dc.subject (關鍵詞) | corrected confidence stes | en_US |
| dc.subject (關鍵詞) | Monte Carlo method | en_US |
| dc.subject (關鍵詞) | difference quotient method | en_US |
| dc.title (題名) | 門檻式自動迴歸模型參數之近似信賴區間 | zh_TW |
| dc.title (題名) | Approximate confidence sets for parameters in a threshold autoregressive model | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | J. Andel and T. Barton. A note on the threshold AR(1) model with cauchy innovations. Journal of Time Series Analysis, 7:1--5, 1986. | zh_TW |
| dc.relation.reference (參考文獻) | J. Andel, I. Netuka and K. Zvara. On the threshold autoregressive processes. Kybernetika, Vol. 20, No. 2 89--106, 1984. | zh_TW |
| dc.relation.reference (參考文獻) | P. J. Brockwell and R. A. Davis. Time Series: Theory and Method. Springer, New York, 1991. | zh_TW |
| dc.relation.reference (參考文獻) | K. S. Chan. Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. | zh_TW |
| dc.relation.reference (參考文獻) | Annals of Statistics, 21:520--533, 1993. | zh_TW |
| dc.relation.reference (參考文獻) | K. S. Chan and H. Tong. On estimating thresholds in autoregressive models. Journal of Time Series Analysis, Vol. 7, No. 3, 179--191, 1986. | zh_TW |
| dc.relation.reference (參考文獻) | K. S. Chan and R. S. Tsay. Limiting properties of the least squares estimator of a continuous threshold autoregressive model. Biometrika 85, 413--426, 1998. | zh_TW |
| dc.relation.reference (參考文獻) | W. S. Chen and C. Lee. Bayesian inference of threshold autoregressive models. Journal of Time Series Analysis, Vol. 16, No. 5, 483--492, 1995. | zh_TW |
| dc.relation.reference (參考文獻) | B. R. Chen and R. S. Tsay. On the ergodicity of TAR(1) processes. The Annals of Applied Probability, 1:613--634, 1991. | zh_TW |
| dc.relation.reference (參考文獻) | D. S. Coad and M. B. Woodroofe. Approximate bias calculations for sequentially designed experiments. Sequential Analysis, 17, 1--31, 1998. | zh_TW |
| dc.relation.reference (參考文獻) | L. Dumbgen. The asymptotic behavior of some nonparametric change point estimators. The Annals of Statistics, 19:1471--1495, 1991. | zh_TW |
| dc.relation.reference (參考文獻) | J.R. Eisele. The doubly adaptive biased coin design for sequential clinical trials. Journal of Statistical Planning and Inference, 38:249--262, 1994. | zh_TW |
| dc.relation.reference (參考文獻) | B. Efron. Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7:1--26, 1979. | zh_TW |
| dc.relation.reference (參考文獻) | W. Enders, B. Falk and P. L. Siklos. A threshold model of real U.S. GDP and the problem of constructing confidence intervals in TAR models. Studies in Nonlinear Dynamics and Econometrics, Vol. 11: No. 3, Article 4, 2007. | zh_TW |
| dc.relation.reference (參考文獻) | J. Gonzalo and M. Wolf. Subsampling inference in threshold autoregressive models. Journal of Econometrics, Vol. 127, Issue 2, 201:224, 2005. | zh_TW |
| dc.relation.reference (參考文獻) | P. Hall. The bootstrap and edgeworth expansion. Springer-Verlag, New York, 1992. | zh_TW |
| dc.relation.reference (參考文獻) | B. E. Hansen. Inference in TAR models. Studies in Nonlinear Dynamics and Econometrics, 1:119--131, 1997. | zh_TW |
| dc.relation.reference (參考文獻) | T. L. Lai and C. Z. Wei. Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Annals of Statistics, 10:154--166, 1982. | zh_TW |
| dc.relation.reference (參考文獻) | W. Loges. The stationary marginal distribution of a threshold AR(1) process. Journal of Time Series Analysis, 25:103--125, 2004. | zh_TW |
| dc.relation.reference (參考文獻) | J. Petrucelli and S. Woolford. A threshold AR(1) model. Journal of Applied Probability, 21:270--286, 1984. | zh_TW |
| dc.relation.reference (參考文獻) | S. M. Potter. A nonlinear approach to US GNP. Journal of Applied Econometrics, Vol. 10, 109--125, 1995. | zh_TW |
| dc.relation.reference (參考文獻) | R. S. Tasi. Analysis of Financial Time Series. Wiley Series in Probability and Statistics, 2005. | zh_TW |
| dc.relation.reference (參考文獻) | T. Terasvirta. Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association, Vol. 89, No. 425, 208:218, 1994. | zh_TW |
| dc.relation.reference (參考文獻) | H. Tong. On a threshold model. Pattern Recognition and Signal Processing, pp. 101–141. | zh_TW |
| dc.relation.reference (參考文獻) | H. Tong. Threshold Models in Non-linear Time Series. Springer-Verlag, New York, 1983. | zh_TW |
| dc.relation.reference (參考文獻) | H. Tong. Non-linear time series: a dynamical system approach. Oxford University Press, New York, 1990. | zh_TW |
| dc.relation.reference (參考文獻) | R. C. Weng and M. Woodroofe. Approximate confidence sets for a stationary AR(p) process. Journal of Statistical Planning and Inference, 136:2719--2745, 2006. | zh_TW |
| dc.relation.reference (參考文獻) | M. Woodroofe. Very weak expansions for sequentially confidence intervals. Annals of Statistics, Vol. 14, No. 3 1049--1067, 1986. | zh_TW |
| dc.relation.reference (參考文獻) | M. Woodroofe. Very weak expansions for sequentially designed experiments: linear models. Annals of Statistics, 17:1087--1102, 1989. | zh_TW |
| dc.relation.reference (參考文獻) | M. Woodroofe and D. S. Coad. Corrected confidence sets for sequentially designed experiments. Statistica Sinica, 7:53--74, 1997. | zh_TW |
| dc.relation.reference (參考文獻) | M. Woodroofe and D. S. Coad. Corrected confidence sets for sequentially designed experiments: Examples. In S. Ghosh, editor. Multivariate Analysis, Design of Experiments, and Survey Sampling, 135--161, New York, 1999. Marcel Dekker, Inc. | zh_TW |
| dc.relation.reference (參考文獻) | Y. C. Yao. Approximating the distribution of the ML estimate of the change-point in a sequence of independent r.v.`s. Annals of Statistics, 3:1321--1328, 1987. | zh_TW |
