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    題名: 門檻式自動迴歸模型參數之近似信賴區間
    Approximate confidence sets for parameters in a threshold autoregressive model
    作者: 陳慎健
    Chen, Shen Chien
    貢獻者: 翁久幸
    Weng, Chiu Hsing
    陳慎健
    Chen, Shen Chien
    關鍵詞: 門檻式自動迴歸模型
    非常弱近似法
    適性化線性模型
    修正信賴區間
    蒙地卡羅法
    差分法
    threshold autoregressive model
    very weak approximation
    adaptive linear model
    corrected confidence stes
    Monte Carlo method
    difference quotient method
    日期: 2008
    上傳時間: 2009-09-18 20:11:16 (UTC+8)
    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。
    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.
    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.
    J. Andel, I. Netuka and K. Zvara. On the threshold autoregressive processes. Kybernetika, Vol. 20, No. 2 89--106, 1984.
    P. J. Brockwell and R. A. Davis. Time Series: Theory and Method. Springer, New York, 1991.
    K. S. Chan. Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model.
    Annals of Statistics, 21:520--533, 1993.
    K. S. Chan and H. Tong. On estimating thresholds in autoregressive models. Journal of Time Series Analysis, Vol. 7, No. 3, 179--191, 1986.
    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.
    W. S. Chen and C. Lee. Bayesian inference of threshold autoregressive models. Journal of Time Series Analysis, Vol. 16, No. 5, 483--492, 1995.
    B. R. Chen and R. S. Tsay. On the ergodicity of TAR(1) processes. The Annals of Applied Probability, 1:613--634, 1991.
    D. S. Coad and M. B. Woodroofe. Approximate bias calculations for sequentially designed experiments. Sequential Analysis, 17, 1--31, 1998.
    L. Dumbgen. The asymptotic behavior of some nonparametric change point estimators. The Annals of Statistics, 19:1471--1495, 1991.
    J.R. Eisele. The doubly adaptive biased coin design for sequential clinical trials. Journal of Statistical Planning and Inference, 38:249--262, 1994.
    B. Efron. Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7:1--26, 1979.
    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.
    J. Gonzalo and M. Wolf. Subsampling inference in threshold autoregressive models. Journal of Econometrics, Vol. 127, Issue 2, 201:224, 2005.
    P. Hall. The bootstrap and edgeworth expansion. Springer-Verlag, New York, 1992.
    B. E. Hansen. Inference in TAR models. Studies in Nonlinear Dynamics and Econometrics, 1:119--131, 1997.
    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.
    W. Loges. The stationary marginal distribution of a threshold AR(1) process. Journal of Time Series Analysis, 25:103--125, 2004.
    J. Petrucelli and S. Woolford. A threshold AR(1) model. Journal of Applied Probability, 21:270--286, 1984.
    S. M. Potter. A nonlinear approach to US GNP. Journal of Applied Econometrics, Vol. 10, 109--125, 1995.
    R. S. Tasi. Analysis of Financial Time Series. Wiley Series in Probability and Statistics, 2005.
    T. Terasvirta. Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association, Vol. 89, No. 425, 208:218, 1994.
    H. Tong. On a threshold model. Pattern Recognition and Signal Processing, pp. 101–141.
    H. Tong. Threshold Models in Non-linear Time Series. Springer-Verlag, New York, 1983.
    H. Tong. Non-linear time series: a dynamical system approach. Oxford University Press, New York, 1990.
    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.
    M. Woodroofe. Very weak expansions for sequentially confidence intervals. Annals of Statistics, Vol. 14, No. 3 1049--1067, 1986.
    M. Woodroofe. Very weak expansions for sequentially designed experiments: linear models. Annals of Statistics, 17:1087--1102, 1989.
    M. Woodroofe and D. S. Coad. Corrected confidence sets for sequentially designed experiments. Statistica Sinica, 7:53--74, 1997.
    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.
    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.
    描述: 博士
    國立政治大學
    統計研究所
    91354503
    97
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0913545031
    資料類型: thesis
    顯示於類別:[統計學系] 學位論文

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