• Abstract: The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow for the presence of the cross-sectional correlation even after taking out common factors. The sparse covariance is estimated by the adaptive thresholding technique as in Cai and Liu (2011). The covariance matrix of the outcome is then estimated based on the factor structure. It is shown that the estimated covariance matrix is still nonsingular regardless of its dimensionality, and is consistent under various norms.

• Paper: pdf file

• Slides: pdf file

• Related literature:

  Fan, Fan and Lv (2008)
  High dimensional covariance matrix estimation using a factor model.
  Journal of Econometrics. 147, 186-197.

  Cai and Liu (2011)
  Adaptive thresholding for sparse covariance matrix estimation.
  JASA.106, 672-684.

• Presentations:

  2011

  • University of Maryland
  • Cornell University, Joint Econometrics and Statistics
  • Northwestern University, Department of Statistics