Controlling False Discovery Rates under Cross-Sectional Correlations

TL;DR

This paper introduces a new method for controlling false discovery rates in multiple hypothesis testing with correlated data, particularly in financial contexts, demonstrating improved power and proven FDR control.

Contribution

It proves the consistency of Fama and French's method under multiple testing and proposes a novel double bootstrap approach for better false discovery control.

Findings

The new method outperforms existing approaches in simulations.

It effectively controls false discovery rate in correlated data.

Application to real financial data validates its practical utility.

Abstract

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.