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<p>This thesis discusses novel developments in Bayesian analytics for high-dimensional
multivariate time series. The focus is on the class of multiregression dynamic models
(MDMs), which can be decomposed into sets of univariate models processed in parallel
yet coupled for forecasting and decision making. Parallel processing greatly speeds
up the computations and vastly expands the range of time series to which the analysis
can be applied. </p><p>I begin by defining a new sparse representation of the dependence
between the components of a multivariate time series. Using this representation, innovations
involve sparse dynamic dependence networks, idiosyncrasies in time-varying auto-regressive
lag structures, and flexibility of discounting methods for stochastic volatilities.</p><p>For
exploration of the model space, I define a variant of the Shotgun Stochastic Search
(SSS) algorithm. Under the parallelizable framework, this new SSS algorithm allows
the stochastic search to move in each dimension simultaneously at each iteration,
and thus it moves much faster to high probability regions of model space than does
traditional SSS. </p><p>For the assessment of model uncertainty in MDMs, I propose
an innovative method that converts model uncertainties from the multivariate context
to the univariate context using Bayesian Model Averaging and power discounting techniques.
I show that this approach can succeed in effectively capturing time-varying model
uncertainties on various model parameters, while also identifying practically superior
predictive and lucrative models in financial studies. </p><p>Finally I introduce common
state coupled DLMs/MDMs (CSCDLMs/CSCMDMs), a new class of models for multivariate
time series. These models are related to the established class of dynamic linear models,
but include both common and series-specific state vectors and incorporate multivariate
stochastic volatility. Bayesian analytics are developed including sequential updating,
using a novel forward-filtering-backward-sampling scheme. Online and analytic learning
of observation variances is achieved by an approximation method using variance discounting.
This method results in faster computation for sequential step-ahead forecasting than
MCMC, satisfying the requirement of speed for real-world applications. </p><p>A motivating
example is the problem of short-term prediction of electricity demand in a "Smart
Grid" scenario. Previous models do not enable either time-varying, correlated structure
or online learning of the covariance structure of the state and observational evolution
noise vectors. I address these issues by using a CSCMDM and applying a variance discounting
method for learning correlation structure. Experimental results on a real data set,
including comparisons with previous models, validate the effectiveness of the new
framework.</p>
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