The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation
University of Zurich, Department of Economics, Working Paper No. 323, Revised version
42 Pages Posted: 1 Jun 2019 Last revised: 4 Feb 2020
Date Written: February 2020
Many econometric and data-science applications require a reliable estimate of the covariance matrix, such as Markowitz 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 paper, 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.
Keywords: Dynamic conditional correlations, factor models, large-dimensional asymptotics, Markowitz portfolio selection, rotation equivariance
JEL Classification: C13, C58, G11
Suggested Citation: Suggested Citation