Efficient Estimation of Approximate Factor Models via Regularized Maximum Likelihood

57 Pages Posted: 27 Sep 2012 Last revised: 30 Sep 2012

See all articles by Jushan Bai

Jushan Bai

New York University (NYU) - Department of Economics

Yuan Liao

Rutgers, The State University of New Jersey - New Brunswick/Piscataway

Date Written: September 26, 2012

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

JEL Classification: C31, C33

Suggested Citation

Bai, Jushan and Liao, Yuan, Efficient Estimation of Approximate Factor Models via Regularized Maximum Likelihood (September 26, 2012). Available at SSRN: https://ssrn.com/abstract=2152416 or http://dx.doi.org/10.2139/ssrn.2152416

Jushan Bai

New York University (NYU) - Department of Economics ( email )

269 Mercer Street, 7th Floor
New York, NY 10003
United States

Yuan Liao (Contact Author)

Rutgers, The State University of New Jersey - New Brunswick/Piscataway ( email )

94 Rockafeller Road
New Brunswick, NJ 08901
United States

HOME PAGE: http://rci.rutgers.edu/~yl1114

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