Title: "A Bayesian Functional Dynamic Linear Model."
We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in our data--a functional component, a time series component, and a multivariate component--we adapt the hierarchical dynamic linear model framework for multivariate time-series data to the functional data setting. For the functional component, we extend Bayesian spline theory to a more general constrained optimization framework, in which the constraints are made explicit in the prior distribution. The resulting estimates are smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of these components, provides exact inference (up to MCMC error) on specific parameters, and readily extends to more general dependence structures. Sampling from the posterior distribution can be accomplished with a straightforward Gibbs sampler. We apply our model to multi-economy yield curve data to demonstrate the flexibility, accuracy, and interpretability of the proposed methods