A Bayesian Multivariate Functional Dynamic Linear Model

TL;DR

This paper introduces a Bayesian multivariate functional dynamic linear model that captures complex dependencies in functional data, enabling joint inference, interpretable basis functions, and applications in economics and neuroscience.

Contribution

It extends hierarchical dynamic linear models to the functional data setting and develops Bayesian spline theory for constrained optimization, providing a flexible framework for multivariate dependent functional data.

Findings

Effective modeling of yield curve data during recession

Application to multivariate brain signal analysis

Efficient Gibbs sampling algorithm for posterior inference

Abstract

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the functional observations, which is smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of the model parameters, provides exact inference (up to MCMC error) on specific parameters, and allows generalized dependence structures. Sampling from the posterior distribution is accomplished with an efficient Gibbs sampling algorithm. We illustrate the proposed framework with two applications: (1) multi-economy yield curve data from the recent global recession, and (2) local field potential brain signals in rats, for which we develop a multivariate functional time series approach for multivariate time-frequency analysis. Supplementary materials, including R code and the multi-economy yield curve data, are available online.