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A Grouped Factor Model

Chen, Pu (2010): A Grouped Factor Model.

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Abstract

In this paper we present a grouped factor model that is designed to explore grouped structures in factor models. We develop an econometric theory consisting of a consistent classification rule to assign variables to their respective groups and a class of consistent model selection criteria to determine the number of groups as well as the number of factors in each group. As a result, we propose a procedure to estimate grouped factor models, in which the unknown number of groups, the unknown relationship between variables to their groups as well as the unknown number of factors in each group are statistically determined based on observed data. The procedure can help to estimate common factor that are pervasive across all groups and group-specific factors that are pervasive only in the respective groups. Simulations show that our proposed estimation procedure has satisfactory finite sample properties.

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