DOUBLY CONSTRAINED FACTOR MODELS WITH APPLICATIONS

Abstract

This paper focuses on factor analysis of multivariate time series. We propose statistical methods that enable analysts to leverage their prior knowledge or substantive information to sharpen the estimation of common factors. Specifically, we consider a doubly constrained factor model that enables analysts to specify both row and column constraints of the data matrix to improve the estimation of common factors. The row constraints may represent classifications of individual subjects whereas the column constraints may show the categories of variables. We derive both the maximum likelihood and least squares estimates of the proposed doubly constrained factor model and use simulations to study the performance of the analysis in finite samples. The Akaike information criterion is used for model selection. Monthly U.S. housing start data from nine geographical divisions are used to demonstrate the application of the proposed model.