Efficient Estimation of Approximate Factor Models via Regularized Maximum Likelihood
57 Pages Posted: 27 Sep 2012 Last revised: 30 Sep 2012
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: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Systemic Risk and Stability in Financial Networks
By Daron Acemoglu, Asuman E. Ozdaglar, ...
-
Systemic Risk and Stability in Financial Networks
By Daron Acemoglu, Asuman E. Ozdaglar, ...
-
Innovation, Reallocation and Growth
By Daron Acemoglu, Ufuk Akcigit, ...
-
Growth Through Heterogeneous Innovations
By Ufuk Akcigit and William Kerr
-
Growth Through Heterogeneous Innovations
By Ufuk Akcigit and William Kerr
-
Growth Through Heterogeneous Innovations
By Ufuk Akcigit and William Kerr
-
Growth Through Heterogeneous Innovations
By Ufuk Akcigit and William Kerr
-
Growth Through Heterogeneous Innovations
By Ufuk Akcigit and William Kerr
-
Innovation by Entrants and Incumbents
By Daron Acemoglu and Dan Cao
-
Innovation by Entrants and Incumbents
By Daron Acemoglu and Dan Cao