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研究生： 羅少廷
Lo, Shao-Ting
論文名稱： 時間序列之逆迴歸降維法
Dimension reduction in time series regression model
指導教授： 周若珍
Chou, Rouh-Jane
口試委員:
學位類別： 博士
Doctor
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： 80
中文關鍵詞： 反切迴歸 、動態反切迴歸
外文關鍵詞： sliced inverse regression, dynamical sliced inverse regression
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    • 在獨立資料下，Li（1991）和Bura and Cook（2001）分別提出sliced inverse regression（SIR）和parametric inverse regression（PIR）方法，利用逆迴歸的方法以達到降低自變數X維的目的。對於時間序列數據， Xia et al.（2002）提出minimum average variance estimation （MAVE）法，除適用於時間序列資料外，亦可應用於獨立資料；Becker et al.（2000）和Huang（2006）分別將SIR法和PIR法延伸，將解釋變數的當期和前期指標皆置於自變數中。本論文探討這種延伸可能的問題，並提出dynamical sliced inverse regression（DSIR）法和dynamical parametric inverse regression（DPIR）法，達到降維之目的。除完成DSIR法和DPIR法的理論基礎外，並以模擬實驗比較二者與MAVE之維度與方向估計，發現DSIR法優於DPIR法和MAVE法。最後，本文以幾個實例展示各法的預測能力。

    Regression analysis is a popular way of studying the relationship between a response variable y and its explanatory variables X. As the dimension of X gets higher, we need to have a gigantic sample. Li (1991) and Bura and Cook (2001) proposed SIR (sliced inverse regression) and PIR (parametric inverse regression) methods respectively to reduce the dimension of explanatory variables for independent data. For time series, Xia et al. (2002) proposed MAVE (minimum average variance estimation) method. The method is applicable for time series and independent data both. Becker et al. (2000) and Huang (2006) extended SIR and PIR to time dependent data by adding the lagged variables into explanatory variables. In this dissertation, we discuss the issue of the extension and propose DSIR (dynamical SIR) and DPIR (dynamical PIR) methods to reduce dimension. We complete the theoretical foundations of DSIR and DPIR methods. Show the efficiency by simulation. Simulation studies show that both outperforms MAVE in estimation dimensionality. Finally, we display their forecasting performances by some empirical studies.

    目錄 1 緒論 1 2 文獻回顧 　 　4 2.1 SIR方法...........................................................................................4 2.2 SAVE方法........................................................................................6 2.3 DAME方法......................................................................................6 2.4 PIR方法...........................................................................................6 2.5 MAVE方法......................................................................................8 2.6 DSIR方法.........................................................................................9 3 時間序列資料之降維度法 10 3.1 DSIR方法的介紹...........................................................................10 3.2 方向估計與模擬分析...................................................................13 3.2.1 等價向量..............................................................................13 3.2.2 模擬實驗分析......................................................................15 3.3 DSIR方法的修正與模擬分析.......................................................20 3.4 DPIR方法的介紹與其修正和模擬...............................................23 3.4.1 DPIR方法的介紹..................................................................23 3.4.2 DPIR方法的修正與模擬分析..............................................26 3.5 DSIR方法、DPIR方法與MAVE方法之比較...............................28 3.5.1 MAVE方法的模擬實驗分析...............................................28 3.5.2 修正後的DSIR、DPIR方法與MAVE方法之比較.............29 3.6 修正後DSIR方法之函數估計.....................................................31 4 實證研究分析 37 4.1 汙染和氣候對循環及呼吸病人的影響之實證分析...................37 4.2 台積電股價投資報酬率之實證分析...........................................46 4.3 台灣失業率之實證分析...............................................................55 5 結論探討 64 附錄 68 參考文獻 77

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