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dc.contributor.authorKowal, Daniel Ryan
dc.identifier.otherbibid: 10361642
dc.description.abstractWe introduce new Bayesian methodology for modeling functional and time series data. While broadly applicable, the methodology focuses on the challenging cases in which (1) functional data exhibit additional dependence, such as time dependence or contemporaneous dependence; (2) functional or time series data demonstrate local features, such as jumps or rapidly-changing smoothness; and (3) a time series of functional data is observed sparsely or irregularly with non-negligible measurement error. A unifying characteristic of the proposed methods is the employment of the dynamic linear model (DLM) framework in new contexts to construct highly efficient Gibbs sampling algorithms. To model dependent functional data, we extend DLMs for multivariate time series data to the functional data setting, and identify a smooth, time-invariant functional basis for the functional observations. The proposed model provides flexible modeling of complex dependence structures among the functional observations, such as time dependence, contemporaneous dependence, stochastic volatility, and covariates. We apply the model to multi-economy yield curve data and local field potential brain signals in rats. For locally adaptive Bayesian time series and regression analysis, we propose a novel class of dynamic shrinkage processes. We extend a broad class of popular global-local shrinkage priors, such as the horseshoe prior, to the dynamic setting by allowing the local scale parameters to depend on the history of the shrinkage process. We prove that the resulting processes inherit desirable shrinkage behavior from the non-dynamic analogs, but provide additional locally adaptive shrinkage properties. We demonstrate the substantial empirical gains from the proposed dynamic shrinkage processes using extensive simulations, a Bayesian trend filtering model for irregular curve-fitting of CPU usage data, and an adaptive time-varying parameter regression model, which we employ to study the dynamic relevance of the factors in the Fama-French asset pricing model. Finally, we propose a hierarchical functional autoregressive (FAR) model with Gaussian process innovations for forecasting and inference of sparsely or irregularly sampled functional time series data. We prove finite-sample forecasting and interpolation optimality properties of the proposed model, which remain valid with the Gaussian assumption relaxed. We apply the proposed methods to produce highly competitive forecasts of daily U.S. nominal and real yield curves.
dc.rightsAttribution 4.0 International*
dc.subjectGaussian Process
dc.subjectHierarchical Bayes
dc.subjectYield Curve
dc.subjectDynamic Linear Model
dc.subjectFactor Model
dc.titleBayesian Methods for Functional and Time Series Data
dc.typedissertation or thesis University of Philosophy D., Statistics
dc.contributor.chairRuppert, David
dc.contributor.committeeMemberMatteson, David
dc.contributor.committeeMemberJarrow, Robert A.
dc.contributor.committeeMemberWells, Martin Timothy

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Except where otherwise noted, this item's license is described as Attribution 4.0 International