| Recently the factor model has gained popularity among empirical researchers because it provides a convenient way to summarize information in large data sets. While the development of the theory can proceed without a complete specification of how many factors there are and what they are, empirical testing does not have such luxury. This lack of specifications poses two immediate problems for empirical research, particularly in testing theories and forecasting exercises: how many factors are appropriate and which factors should be selected. This dissertation seeks to address these issues.;Existing methods of order selection for choosing the number of factors are designed primarily for small or large dimensional factor models. Their performances tend to deteriorate when the cross section size N is moderately large (say, 20 ≤ N ≤ 40). Chapter II uses a quasi-maximum likelihood framework to design model selection procedure based on the Posterior Information criteria (PIC) (Phillips and Ploberger, 1996) to determine the factor count. It is shown that the factor count can be consistently estimated using PIC in both small and large factor models. Moreover, the PIC tends to outperform existing criteria especially when N lies between 20 and 40.;Chapter III derives the rate of convergence and the limiting distributions of both estimated factor loadings and factors. Our estimators for factors are more efficient than principal component estimators. In addition, it is found the forecasts based on the extracted factors of Quasi-maximum likelihood method enjoy efficiency gains over principal component estimators for factor spaces when the cross section size passes to infinity more slowly than the time dimension. |
