Fall 2009 Thursday, September 24   Speaker: Ruey Tsay Ph.D. Title: "Constrained Factor Models: Estimation and Applications" Abstract: (Joint with Henghsiu Tsai, Institute of Statistical Science, Academia Sinica). This paper considers estimation and applications of constrained and partially constrained approximate factor models when the dimension of explanatory variables is high. It derives likelihood ratio test for the constraints under normality. It also shows that the least squares estimation is based on constrained principal component analysis and provides consistent estimates for the model under certain conditions. The normality condition is not used for the least squares estimation. The constraints are useful tools to incorporate prior information or substantive theory in empirical applications of approximate factor models. In addition, the constraints also serve as a statistical tool to obtain parsimonious econometric models for forecasting, to simplify the interpretations of the common factors, and to reduce the dimension. We use simulation and real examples to investigate the performance of constrained estimation in finite samples and to highlight the importance of noise-to-signal ratio in factor analysis. We also compare the constrained model with its unconstrained counterpart both in estimation and in forecasting. Two real examples are shown.

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