Factor-adjusted multiple testing of correlations

Both global and multiple testing procedures have previously been proposed to untangle the correlation structures among high-dimensional data. In this article, we extend the results of both tests to learn the correlations of the factor-adjusted residuals in an approximate factor model, which can be used to simultaneously detect the highly matched pairs of stocks in finance. The factor-adjusted residuals are not observed and estimated using the method of principal components. We theoretically investigate the effects of estimating the factor-adjusted residuals on the subsequent global and multiple testing procedures. Furthermore, we demonstrate that the correlation structure of the factor-adjusted residuals can be recovered if appropriate thresholds are used in the proposed multiple testing procedure. Extensive simulation studies and a real data analysis are presented in which the proposed method is applied to select stock pairs in China's stock market.