Multiple Testing under High-dimensional Dynamic Factor Model

Abstract

Large-scale multiple testing under static factor models is widely used to detect sparse signals in high-dimensional data. However, static factor models are arguably too stringent because they ignore serial correlation, which seriously distorts error rate control in large-scale inference. In this manuscript, we propose a new multiple testing procedure under dynamic factor models that is robust to nonlinear serial dependence. The idea is to integrate a new sample-splitting strategy based on chronological order and a two-pass Fama--Macbeth regression to form a series of test statistics with marginal symmetry properties and then to use these properties to obtain a data-driven threshold. We show that our procedure can control the false discovery rate asymptotically under high-dimensional dynamic factor models. {As a byproduct of independent interest, we establish a new exponential-type deviation inequality for the sum of random variables over various functionals of linear and nonlinear processes.} Our numerical results, including a case study on hedge fund selection, demonstrate the advantage of our proposed method over several state-of-the-art methods.