  Its conceptual appeal and effectiveness has made latent factor modeling an
indispensable tool for multivariate analysis. Despite its popularity across
many fields, there are outstanding methodological challenges that have hampered
practical deployments. One major challenge is the selection of the number of
factors, which is exacerbated for dynamic factor models, where factors can
disappear, emerge, and/or reoccur over time. Existing tools that assume a fixed
number of factors may provide a misguided representation of the data mechanism,
especially when the number of factors is crudely misspecified. Another
challenge is the interpretability of the factor structure, which is often
regarded as an unattainable objective due to the lack of identifiability.
Motivated by a topical macroeconomic application, we develop a flexible
Bayesian method for dynamic factor analysis (DFA) that can simultaneously
accommodate a time-varying number of factors and enhance interpretability
without strict identifiability constraints. To this end, we turn to dynamic
sparsity by employing Dynamic Spike-and-Slab (DSS) priors within DFA. Scalable
Bayesian EM estimation is proposed for fast posterior mode identification via
rotations to sparsity, enabling Bayesian data analysis at scales that would
have been previously time-consuming. We study a large-scale balanced panel of
macroeconomic variables covering multiple facets of the US economy, with a
focus on the Great Recession, to highlight the efficacy and usefulness of our
proposed method.
