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Efficient Estimation of Approximate Factor Models

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  • Bai, Jushan
  • Liao, Yuan

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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 41558.

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Date of creation: Sep 2012
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Handle: RePEc:pra:mprapa:41558

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Keywords: High dimensionality; unknown factors; principal components; sparse matrix; conditional sparse; thresholding; cross-sectional correlation; penalized maximum likelihood; adaptive lasso; heteroskedasticity;

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  1. Forni, Mario & Lippi, Marco, 2000. "The Generalized Dynamic Factor Model: Representation Theory," CEPR Discussion Papers, C.E.P.R. Discussion Papers 2509, C.E.P.R. Discussion Papers.
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Cited by:
  1. Matteo Barigozzi & Christian Brownlees, 2013. "Nets: Network Estimation for Time Series," Working Papers 723, Barcelona Graduate School of Economics.
  2. Cheng, Xu & Liao, Zhipeng & Schorfheide, Frank, 2013. "Shrinkage estimation of high-dimensional factor models with structural instabilities," Working Papers 14-4, Federal Reserve Bank of Philadelphia.
  3. Xu Cheng & Zhipeng Liao & Frank Schorfheide, 2014. "Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities," NBER Working Papers 19792, National Bureau of Economic Research, Inc.

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