A Multiple Testing Approach to the Regularisation of Large Sample Correlation Matrices

• Activity Number: 558 - Recent Developments in Statistics of Economic Data in High-Dimensional Contexts
• Type: Invited
• Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Natalia Bailey* and Hashem Pesaran and Vanessa Smith
• Companies: Monash University and University of Southern California and Trinity College, Cambridge and University of York
• Keywords: High-dimensional data ; Multiple testing ; Non-Gaussian observations ; Sparsity ; Thresholding ; Shrinkage

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 maximum degree of dependence of the underlying observations when their pair-wise correlation is zero, 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 favourable when compared to a number of other estimators in the literature when using Monte Carlo experiments.