Macroeconomics

Volatility (finance)

Statistics

Covariance matrix

Materials science

Economics

Estimation of covariance matrices

Shrinkage estimator

Stylized fact

Covariance

Matrix (chemical analysis)

Shrinkage

Mathematics

Estimator

Econometrics

Composite material

Bias of an estimator

Minimum-variance unbiased estimator

Journal of Financial Econometrics

Many econometric and data-science applications require a reliable estimate of the covariance matrix, such as Markowitz’s portfolio selection. When the number of variables is of the same magnitude as the number of observations, this constitutes a difficult estimation problem; the sample covariance matrix certainly will not do. In this article, we review our work in this area, going back 15+ years. We have promoted various shrinkage estimators, which can be classified into linear and nonlinear. Linear shrinkage is simpler to understand, to derive, and to implement. But nonlinear shrinkage can deliver another level of performance improvement, especially if overlaid with stylized facts such as time-varying co-volatility or factor models.

The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation