An Overview of the Estimation of Large Covariance and Precision Matrices

32 Pages Posted: 10 May 2016

See all articles by Jianqing Fan

Jianqing Fan

Princeton University - Bendheim Center for Finance

Yuan Liao

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

Han Liu

Princeton University - Department of Operations Research & Financial Engineering (ORFE)

Date Written: February 2016

Abstract

The estimation of large covariance and precision matrices is fundamental in modern multivariate analysis. However, problems arise from the statistical analysis of large panel economic and financial data. The covariance matrix reveals marginal correlations between variables, while the precision matrix encodes conditional correlations between pairs of variables given the remaining variables. In this paper, we provide a selective review of several recent developments on the estimation of large covariance and precision matrices. We focus on two general approaches: a rank‐based method and a factor‐model‐based method. Theories and applications of both approaches are presented. These methods are expected to be widely applicable to the analysis of economic and financial data.

Keywords: Approximate factor model, Elliptical distribution, Graphical model, Heavy‐tailed, High‐dimensionality, Low‐rank matrix, Principal components, Rank‐based methods, Sparse matrix, Thresholding

Suggested Citation

Fan, Jianqing and Liao, Yuan and Liu, Han, An Overview of the Estimation of Large Covariance and Precision Matrices (February 2016). The Econometrics Journal, Vol. 19, Issue 1, pp. C1-C32, 2016. Available at SSRN: https://ssrn.com/abstract=2777801 or http://dx.doi.org/10.1111/ectj.12061

Jianqing Fan (Contact Author)

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States
609-258-7924 (Phone)
609-258-8551 (Fax)

HOME PAGE: http://orfe.princeton.edu/~jqfan/

Yuan Liao

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

Han Liu

Princeton University - Department of Operations Research & Financial Engineering (ORFE) ( email )

Sherrerd Hall, Charlton Street
Princeton, NJ 08544
United States

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