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The power of (non-)linear shrinking: a review and guide to covariance matrix estimation


Ledoit, Olivier; Wolf, Michael (2022). The power of (non-)linear shrinking: a review and guide to covariance matrix estimation. Journal of Financial Econometrics, 20(1):187-218.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Uncontrolled Keywords:Economics and econometrics, finance, dynamic conditional correlations, factor models, large-dimensional asymptotics, Markowitz’s portfolio selection, rotation equivariance
Language:English
Date:25 January 2022
Deposited On:05 Feb 2021 11:31
Last Modified:18 Mar 2022 09:52
Publisher:Oxford University Press
ISSN:1479-8409
OA Status:Closed
Publisher DOI:https://doi.org/10.1093/jjfinec/nbaa007
Related URLs:https://www.zora.uzh.ch/id/eprint/170642/

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