摘要：This paper introduces a novel class of Bayesian models for multivariate
time series analysis based on a synthesis of dynamic linear models and graphical
models. The synthesis uses sparse graphical modelling ideas to introduce struc-
tured, conditional independence relationships in the time-varying, cross-sectional
covariance matrices of multiple time series. We de ne this new class of models and
their theoretical structure involving novel matrix-normal/hyper-inverse Wishart
distributions. We then describe the resulting Bayesian methodology and compu-
tational strategies for model tting and prediction. This includes novel stochastic
evolution theory for time-varying, structured variance matrices, and the full se-
quential and conjugate updating, ltering and forecasting analysis. The models are
then applied in the context of nancial time series for predictive portfolio analysis.
The improvements de ned in optimal Bayesian decision analysis in this example
context vividly illustrate the practical bene ts of the parsimony induced via appro-
priate graphical model structuring in multivariate dynamic modelling. We discuss
theoretical and empirical aspects of the conditional independence structures in
such models, issues of model uncertainty and search, and the relevance of this new
framework as a key step towards scaling multivariate dynamic Bayesian modelling
methodology to time series of increasing dimension and complexity.
关键词：Bayesian Forecasting, Dynamic Linear Models, Gaussian Graphical
Models, Graphical Model Uncertainty, Hyper-Inverse Wishart Distribution, Port-
folio Analysis.
