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ESTIMATION OF TIME-VARYING COVARIANCE MATRICES FOR LARGE DATASETS

Published online by Cambridge University Press:  08 February 2021

Yiannis Dendramis ,
Liudas Giraitis  and
George Kapetanios
Yiannis Dendramis
Affiliation:
Athens University of Economics and Business
Liudas Giraitis*
Affiliation:
Queen Mary University of London
George Kapetanios
Affiliation:
King’s College London
*
Corresponding address: School of Economics and Finance, Queen Mary University of London, LondonE1 4NS, UK: e-mail: L.Giraitis@qmul.ac.uk.
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Abstract

Time variation is a fundamental problem in statistical and econometric analysis of macroeconomic and financial data. Recently, there has been considerable focus on developing econometric modelling that enables stochastic structural change in model parameters and on model estimation by Bayesian or nonparametric kernel methods. In the context of the estimation of covariance matrices of large dimensional panels, such data requires taking into account time variation, possible dependence and heavy-tailed distributions. In this paper, we introduce a nonparametric version of regularization techniques for sparse large covariance matrices, developed by Bickel and Levina (2008) and others. We focus on the robustness of such a procedure to time variation, dependence and heavy-tailedness of distributions. The paper includes a set of results on Bernstein type inequalities for dependent unbounded variables which are expected to be applicable in econometric analysis beyond estimation of large covariance matrices. We discuss the utility of the robust thresholding method, comparing it with other estimators in simulations and an empirical application on the design of minimum variance portfolios.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 6 , December 2021 , pp. 1100 - 1134
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

We thank the Editor, the Co-Editor and the Referees for constructive comments. Yiannis Dendramis acknowledges support from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 708501.

References

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