  Large-scale multiple testing under static factor models is commonly used to
select skilled funds in financial market. However, static factor models are
arguably too stringent as it ignores the serial correlation, which severely
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 against both heavy-tailed distributions and the 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 statistics
with marginal symmetry properties and then to utilize the symmetry properties
to obtain a data-driven threshold. We show that our procedure is able to
control the false discovery rate (FDR) asymptotically under high-dimensional
dynamic factor models. As a byproduct that is of independent interest, we
establish a new exponential-type deviation inequality for the sum of random
variables on a variety of functionals of linear and non-linear processes.
Numerical results including a case study on hedge fund selection demonstrate
the advantage of the proposed method over several state-of-the-art methods.
