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A multiple testing approach to the regularisation of large sample correlation matrices

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JournalJournal of Econometrics
DateAccepted/In press - 19 Oct 2018
DateE-pub ahead of print - 5 Nov 2018
DatePublished (current) - 1 Feb 2019
Issue number2
Volume208
Number of pages28
Pages (from-to)507-534
Early online date5/11/18
Original languageEnglish

Abstract

This paper proposes a regularisation method for the estimation of large covariance matrices that uses insights from the multiple testing (MT) literature. The approach tests the statistical significance of individual pair-wise correlations and sets to zero those elements that are not statistically significant, taking account of the multiple testing nature of the problem. The effective p-values of the tests are set as a decreasing function of N (the cross section dimension), the rate of which is governed by the nature of dependence of the underlying observations, and the relative expansion rates of N and T (the time dimension). In this respect, the method specifies the appropriate thresholding parameter to be used under Gaussian and non-Gaussian settings. The MT estimator of the sample correlation matrix is shown to be consistent in the spectral and Frobenius norms, and in terms of support recovery, so long as the true covariance matrix is sparse. The performance of the proposed MT estimator is compared to a number of other estimators in the literature using Monte Carlo experiments. It is shown that the MT estimator performs well and tends to outperform the other estimators, particularly when N is larger than T.

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© 2018 Elsevier B.V. All rights reserved. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.

    Research areas

  • High-dimensional data, Multiple testing, Non-Gaussian observations, Shrinkage, Sparsity, Thresholding

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