Abstract
This thesis concerns about some modeling issues for a constrained factor model (Tsai and Tsay, 2010). This model was initially proposed for summarizing high-dimensional variables in a low-dimensional form with a pre-specified constrained structure. First, the static constrained factor model is extended to the dynamic one by incorporating temporal dependence in the common factors. Second, we employ the Expectation and Maximization algorithm to solve the maximum likelihood estimate for a dynamic constrained factor model. In addition, a sequential testing procedure based on likelihood ratio is proposed to determine a suitable dimension for common factors. Finally, we apply the singular value decomposition coupled with several clustering methods to determine the grouping structure among variables in the constraint matrix. Again, the number of clusters is determined via a sequential testing procedure based on likelihood ratio. The performance of the proposed methodology is demonstrated by a simulation study and an application with real data.