Smoothed dynamic factor analysis for identifying trends in multivariate time series

Ecological processes are rarely directly observable, and inference often relies on estimating hidden or latent processes. State-space models have become widely used for this task because of their ability to simultaneously estimate the multiple sources variation (natural variability variance attributed observation errors). For multivariate time series, a second aim is dimension reduction, number that smaller than observed series. Dynamic factor analysis (DFA) has been performing time-series where modelled as random walks. Whereas may be suitable some situations, walks too flexible other cases. Here, we introduce new class models, smooth functions (basis splines, penalized splines Gaussian process models). We implement these in our bayesdfa r package, which uses rstan package fitting. After evaluating model performance with simulated data, apply conventional trend two long-term datasets from west coast United States: (a) 35-year dataset pelagic juvenile rockfishes (b) 39-year fisheries catches. Our simulations demonstrate matching underlying smoothness make better out-of-sample predictions, but advantage diminishes increasing levels error. both case studies, best had higher predictive accuracy, yielded more precise compared approach. The introduced here offer approach state-space reduction These Bayesian particularly useful data clumped time, high signal noise ratios generally assumed relatively smooth.