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Identifying observed factors in approximate factor models: estimation and hypothesis testing

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  • Chen, Liang

Abstract

Despite their popularities in recent years, factor models have long been criticized for the lack of identification. Even when a large number of variables are available, the factors can only be consistently estimated up to a rotation. In this paper, we try to identify the underlying factors by associating them to a set of observed variables, and thus give interpretations to the orthogonal factors estimated by the method of Principal Components. We first propose a estimation procedure to select a set of observed variables, and then test the hypothesis that true factors are exact linear combinations of the selected variables. Our estimation method is shown to able to correctly identity the true observed factor even in the presence of mild measurement errors, and our test statistics are shown to be more general than those of Bai and Ng (2006). The applicability of our methods in finite samples and the advantages of our tests are confirmed by simulations. Our methods are also applied to the returns of portfolios to identify the underlying risk factors.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 37514.

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Date of creation: 20 Mar 2012
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Handle: RePEc:pra:mprapa:37514

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Keywords: factor models; observed factors; estimation; hypothesis testing; Fama-French three factors;

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