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


Ledoit, Olivier; Wolf, Michael (2020). The power of (non-)linear shrinking: a review and guide to covariance matrix estimation. Working paper series / Department of Economics 323, University of Zurich.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C13, C58, G11
Uncontrolled Keywords:Dynamic conditional correlations, factor models, large-dimensional asymptotics, Markowitz portfolio selection, rotation equivariance
Language:English
Date:February 2020
Deposited On:08 May 2019 08:41
Last Modified:03 Feb 2020 16:15
Series Name:Working paper series / Department of Economics
Number of Pages:41
ISSN:1664-705X
Additional Information:Revised version
OA Status:Green
Official URL:https://www.econ.uzh.ch/static/release/workingpapers.php?id=1002

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