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研究生: 張育瑋
Chang, Yu-Wei
論文名稱: TAR模型建模之相關議題
Some Issues on Threshold Autoregressive Modeling
指導教授: 徐南蓉
Hsu, Nan-Jung
口試委員:
學位類別: 碩士
Master
系所名稱: 理學院 - 統計學研究所
Institute of Statistics
論文出版年: 2009
畢業學年度: 97
語文別: 中文
論文頁數: 32
中文關鍵詞: 模型選取TAR modelthreshold 變數
外文關鍵詞: model selection, TAR model, threshold 變數
相關次數: 點閱:3下載:0
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  • TAR模型的建模過程包括參數估計與模型選取。後者包括選取threshold 變數與AR order。threshold 變數選取的好壞,對後續的其他估計步驟有決定性的影響。由F統計量或MLE法選取threshold 變數均相當簡便,然而本文的模擬結果顯示,在某些情況下,兩者選出的threshold 變數並不一定可以進一步適配出有良好預測力的模型,此時配適多個TAR模型再將其預測取平均,可以有效降低PMSE等預測誤差指標。在實證分析上,以類流感、加拿大山貓以及太陽黑子三筆數據作實例探討。


    Parameter estimation and model selection are two main steps in the procedure of modeling threshold autoregressive model. The latter one includes selection of threshold variable and AR order, which play key role in the performance of modeling. Selecting threshold variable according to F statistic proposed by Tsay (1989) or according to method of MLE are two simple and widely used methods. However, it is showed in present study by simulation as well as real data that threshold variables selected by these two methods not necessary brings the fitted model with good prediction performance. Modeling two threshold autoregressive models according to the first two threshold variables chosen by either of the two methods and then averaging the one-step prediction usually decrease PMSE. The ILI, Lynx and sunspot data are used for illustration.

    目 錄 第一章 緒論與文獻回顧 p.1 第二章 Threshold Autoregressive Model與其他相關模型 p.4 2.1 Threshold Autoregressive Model 2.2 TAR model的相關模型 第三章 模擬研究 p.8 3.1 模擬試驗的設定 3.2 模擬試驗的結果 第四章 實證資料研究 p.18 4.1 流感病例數(Influenza-like illness data, ILI data) 4.2 加拿大山貓數量的動態結構(Canadian Lynx data) 4.3 太陽黑子的時間序列數據(sunspot data) 4.4 使用F統計量或者MLE法選模的其他議題 第五章 結論與後續研究 p.31 參考文獻 p.32

    參考文獻

    Elton, C. and Nicholson, M. (1942). The ten-year cycle in numbers of the lynx in Canada. Journal of Animal Ecology, 11, 215–244.
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    Psaradakis, Z., Sola, M., Spagnolo, F. and Spagnolo, N. (2009). Selecting nonlinear time series models using information criteria. Journal of Time Series Analysis, 30(4), 369-394.
    Tong, H. and Lim, K. S. (1980). Threshold Autoregression, Limit Cycles and Cyclical Data (with discussion). Journal of the Royal Statistical Society, Series B, 42, 245-292.
    Tong, H. (1990). Non-linear Time Series: A Dynamical Systems Approach, Oxford University Press, Oxford.
    Tsay, R.S. (1989). Testing and modelling threshold autoregressive processes. Journal of the American Statistical Association, 84, 231–240.
    Wu, S. and Chen, R. (2007). Threshold variable determination and threshold variable driven switching autoregressive models. Statistica Sinica, 17, 241-264.

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