Abstract
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.