TY - JOUR
T1 - A multiple testing approach to the regularisation of large sample correlation matrices
AU - Bailey, Natalia
AU - Pesaran, M. Hashem
AU - Smith, L. Vanessa
PY - 2019/2
Y1 - 2019/2
N2 - 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.
AB - 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.
KW - High-dimensional data
KW - Multiple testing
KW - Non-Gaussian observations
KW - Shrinkage
KW - Sparsity
KW - Thresholding
UR - http://www.scopus.com/inward/record.url?scp=85057963582&partnerID=8YFLogxK
U2 - 10.1016/j.jeconom.2018.10.006
DO - 10.1016/j.jeconom.2018.10.006
M3 - Article
AN - SCOPUS:85057963582
SN - 0304-4076
VL - 208
SP - 507
EP - 534
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 2
ER -