摘要
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。
並列摘要
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.