A Bayesian Model for Dependent Functional Data

• Activity Number: 178
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Daniel Kowal*+ and David Scott Matteson and David Ruppert
• Companies: Cornell University and Cornell University and Cornell University
• Keywords: functional data ; time series ; splines ; yield curves ; optimization ; dynamic linear models

Abstract

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in our data--functional, time dependent, and multivariate components--we extend a hierarchical dynamic linear model framework for multivariate time-series data to the functional data setting. We also 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 allows generalized dependence structures. Sampling from the posterior distribution can be accomplished with an efficient Gibbs sampling algorithm. We illustrate the proposed framework by modeling multi-economy yield curve data from the recent global financial crisis and discuss the flexibility, accuracy, and interpretability of the proposed methods.