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

46 Pages Posted: 3 Jul 2014

See all articles by Natalia Bailey

Natalia Bailey

Monash University

M. Hashem Pesaran

University of Southern California - Department of Economics; University of Cambridge - Trinity College (Cambridge)

L. Vanessa Smith

University of York - Department of Economics and Related Studies

Date Written: June 11, 2014

Abstract

This paper proposes a novel regularisation method for the estimation of large covariance matrices, which makes use of insights from the multiple testing literature. The method 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 procedure is straightforward to implement, and does not require cross validation. By using the inverse of the normal distribution at a predetermined significance level, it circumvents the challenge of evaluating the theoretical constant arising in the rate of convergence of existing thresholding estimators. We compare the performance of our multiple testing (MT) estimator to a number of thresholding and shrinkage estimators in the literature in a detailed Monte Carlo simulation study. Results show that our MT estimator performs well in a number of different settings and tends to outperform other estimators, particularly when the cross-sectional dimension, N, is larger than the time series dimension, T: If the inverse covariance matrix is of interest then we recommend a shrinkage version of the MT estimator that ensures positive definiteness.

Keywords: sparse correlation matrices, high-dimensional data, multiple testing, thresholding, shrinkage

JEL Classification: C130, C580

Suggested Citation

Bailey, Natalia and Pesaran, M. Hashem and Smith, L. Vanessa, A Multiple Testing Approach to the Regularisation of Large Sample Correlation Markets (June 11, 2014). CESifo Working Paper Series No. 4834, Available at SSRN: https://ssrn.com/abstract=2461655

Natalia Bailey

Monash University ( email )

23 Innovation Walk
Wellington Road
Clayton, Victoria 3800
Australia

M. Hashem Pesaran (Contact Author)

University of Southern California - Department of Economics

3620 South Vermont Ave. Kaprielian (KAP) Hall 300
Los Angeles, CA 90089
United States

University of Cambridge - Trinity College (Cambridge) ( email )

United Kingdom

L. Vanessa Smith

University of York - Department of Economics and Related Studies ( email )

Heslington
University of York
York, YO10 5DD
United Kingdom

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
25
Abstract Views
272
PlumX Metrics