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Dynamic matrix-variate graphical models

Publication ,  Journal Article
Carvalho, CM; West, M
Published in: Bayesian Analysis
December 1, 2007

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 define 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 fitting and prediction. This includes novel stochastic evolution theory for time-varying, structured variance matrices, and the full se-quential and conjugate updating, filtering and forecasting analysis. The models are then applied in the context of financial time series for predictive portfolio analysis. The improvements defined in optimal Bayesian decision analysis in this example context vividly illustrate the practical benefits 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. © 2007 International Society for Bayesian Analysis.

Duke Scholars

Published In

Bayesian Analysis

DOI

EISSN

1931-6690

ISSN

1936-0975

Publication Date

December 1, 2007

Volume

2

Issue

1

Start / End Page

69 / 98

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics
 

Citation

APA
Chicago
ICMJE
MLA
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Carvalho, C. M., & West, M. (2007). Dynamic matrix-variate graphical models. Bayesian Analysis, 2(1), 69–98. https://doi.org/10.1214/07-BA204
Carvalho, C. M., and M. West. “Dynamic matrix-variate graphical models.” Bayesian Analysis 2, no. 1 (December 1, 2007): 69–98. https://doi.org/10.1214/07-BA204.
Carvalho CM, West M. Dynamic matrix-variate graphical models. Bayesian Analysis. 2007 Dec 1;2(1):69–98.
Carvalho, C. M., and M. West. “Dynamic matrix-variate graphical models.” Bayesian Analysis, vol. 2, no. 1, Dec. 2007, pp. 69–98. Scopus, doi:10.1214/07-BA204.
Carvalho CM, West M. Dynamic matrix-variate graphical models. Bayesian Analysis. 2007 Dec 1;2(1):69–98.

Published In

Bayesian Analysis

DOI

EISSN

1931-6690

ISSN

1936-0975

Publication Date

December 1, 2007

Volume

2

Issue

1

Start / End Page

69 / 98

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics