Controlling False Discovery Rates under Cross-Sectional Correlations
This addresses the challenge of identifying significant factors in financial data with correlated hypotheses, offering improved power over existing methods, though it is incremental in the context of multiple testing literature.
The paper tackles the problem of controlling false discovery rates in multiple hypothesis testing with cross-sectional correlations, particularly in financial asset pricing, by proposing a novel double bootstrapping method that achieves superior statistical power and proven false discovery rate control.
We consider controlling the false discovery rate for testing many time series with an unknown cross-sectional correlation structure. Given a large number of hypotheses, false and missing discoveries can plague an analysis. While many procedures have been proposed to control false discovery, most of them either assume independent hypotheses or lack statistical power. A problem of particular interest is in financial asset pricing, where the goal is to determine which ``factors" lead to excess returns out of a large number of potential factors. Our contribution is two-fold. First, we show the consistency of Fama and French's prominent method under multiple testing. Second, we propose a novel method for false discovery control using double bootstrapping. We achieve superior statistical power to existing methods and prove that the false discovery rate is controlled. Simulations and a real data application illustrate the efficacy of our method over existing methods.