Efficient Estimation of Approximate Factor Models

Jushan Bai and Yuan Liao

MPRA Paper from University Library of Munich, Germany

Abstract: We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the factor loadings or common factors because it essentially treats the idiosyncratic error to be homoskedastic and cross sectionally uncorrelated. For the efficient estimation, it is essential to estimate a large error covariance matrix. We assume the model to be conditionally sparse, and propose two approaches to estimating the common factors and factor loadings; both are based on maximizing a Gaussian quasi-likelihood and involve regularizing a large covariance sparse matrix. In the first approach the factor loadings and the error covariance are estimated separately while in the second approach they are estimated jointly. Extensive asymptotic analysis has been carried out. In particular, we develop the inferential theory for the two-step estimation. Because the proposed approaches take into account the large error covariance matrix, they produce more efficient estimators than the classical PCA methods or methods based on a strict factor model.

Keywords: High dimensionality; unknown factors; principal components; sparse matrix; conditional sparse; thresholding; cross-sectional correlation; penalized maximum likelihood; adaptive lasso; heteroskedasticity (search for similar items in EconPapers)
JEL-codes: C01 C31 C33 (search for similar items in EconPapers)
Date: 2012-09
New Economics Papers: this item is included in nep-cse, nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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