Sequential Cauchy Combination Test for Multiple Testing Problems with Financial Applications

Abstract

We introduce a simple tool to control for false discoveries and identify individual signals in scenarios involving many tests, dependent test statistics, and potentially sparse signals. The tool applies the Cauchy combination test recursively on a sequence of expanding subsets of $p$-values and is referred to as the sequential Cauchy combination test. While the original Cauchy combination test aims to make a global statement about a set of null hypotheses by summing transformed $p$-values, our sequential version determines which $p$-values trigger the rejection of the global null. The sequential test achieves strong familywise error rate control, exhibits less conservatism compared to existing controlling procedures when dealing with dependent test statistics, and provides a power boost. As illustrations, we revisit two well-known large-scale multiple testing problems in finance for which the test statistics have either serial dependence or cross-sectional dependence, namely monitoring drift bursts in asset prices and searching for assets with a nonzero alpha. In both applications, the sequential Cauchy combination test proves to be a preferable alternative. It overcomes many of the drawbacks inherent to inequality-based controlling procedures, extreme value approaches, resampling and screening methods, and it improves the power in simulations, leading to distinct empirical outcomes.