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Activity Number: 68
Type: Topic Contributed
Date/Time: Sunday, July 31, 2016 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #318790
Title: A Bayesian Multivariate Functional Dynamic Linear Model
Author(s): Daniel Ryan Kowal* and David Matteson and David Ruppert
Companies: Cornell University and Cornell University and Cornell University
Keywords: hierarchical Bayes ; orthogonality constraint ; spline ; time-frequency analysis ; yield curve ; time series

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. 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) weekly 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.

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