Testing large dimensional correlation

Abstract

This paper introduces a test for zero correlation in situations where the correlation matrix is large compared to the sample size. The test statistic is the sum of the squared correlation coe±cients in the sample. We derive its limiting null distribution as the number of variables as well as the sample size converge to infinity. A Monte Carlo simulation finds both size and power for finite samples to be suitable. We apply the test to the vector of default rates, a risk factor in portfolio credit risk, in different sectors of the German economy.