Dynamic factor analysis (DFA) is a statistical tool for understanding the latent processes that may be shared amongst a collection of observed multivariate time series. DFA has been widely applied to a number of fields, including economics, medicine, and environmental sciences. We extend conventional DFA to (1) model deviations drawn from a Student-t distribution to better capture extremes, (2) model latent processes (trends) with autoregressive and moving-average components, (3) develop alternative models for the latent trends. While DFA generally models trends as a random walk process, we introduce a new class of models, where latent trends are modeled as smooth functions. These models are applied to two long-term datasets from the west coast of the United States: (1) a 35-year dataset of juvenile rockfishes from the west coast of the United States, and (2) a 39-year dataset of fisheries catches. Estimation and model selection is done in a Bayesian framework using Stan, with code provided as the ‘bayesdfa’ R package.