Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Simultaneous Graphical Dynamic Modeling

Mike West, Luke Vrotsos

TL;DR

This paper surveys simultaneous graphical dynamic linear models (SGDLMs), a flexible framework that combines customized univariate DLMs with sparse time-varying cross-series links to enable scalable Bayesian filtering and forecasting for high-dimensional time series. It develops new theory linking dynamic graphical structure with implicit sparse factor models, and extends Bayesian procedures to handle model uncertainty via marginal likelihoods and to support counterfactual causal forecasting with missing data through Monte Carlo filtering and the outcome adaptive model. The methodology is illustrated through a global GDP dataset, revealing time-varying cross-country relationships and causal effects, with model averaging guiding structure selection and post-intervention inference. The work demonstrates how SGDLMs provide a practical, fully Bayesian approach to causal analysis in high-dimensional time series, with broad implications for macroeconomics and related domains.

Abstract

We review theory and methodology of the class of simultaneous graphical dynamic linear models (SGDLMs) that provide flexibility, parsimony and scalability of multivariate time series analysis. Discussion includes core theoretical aspects and summaries of existing Bayesian methodology for forward filtering and forecasting with SGDLMs. The review is complemented by new theory linking dynamic graphical and factor models, and extensions of the Bayesian methodology. This addresses graphical structure uncertainty via model marginal likelihood evaluation, and analysis with missing data relevant to counterfactual analysis. The latter advances the ability to scale causal analysis to higher-dimensional time series. Aspects of the theory and methodology are exemplified in a global macroeconomic time series study with time-varying cross-series relationships and primary interests in potential causal effects. The example highlights the utility of SGDLMs with insights generated by the theoretical structure of these models, and benefits of fully Bayesian assessment of post-intervention outcomes in causal time series studies as in prediction more generally.

Simultaneous Graphical Dynamic Modeling

TL;DR

This paper surveys simultaneous graphical dynamic linear models (SGDLMs), a flexible framework that combines customized univariate DLMs with sparse time-varying cross-series links to enable scalable Bayesian filtering and forecasting for high-dimensional time series. It develops new theory linking dynamic graphical structure with implicit sparse factor models, and extends Bayesian procedures to handle model uncertainty via marginal likelihoods and to support counterfactual causal forecasting with missing data through Monte Carlo filtering and the outcome adaptive model. The methodology is illustrated through a global GDP dataset, revealing time-varying cross-country relationships and causal effects, with model averaging guiding structure selection and post-intervention inference. The work demonstrates how SGDLMs provide a practical, fully Bayesian approach to causal analysis in high-dimensional time series, with broad implications for macroeconomics and related domains.

Abstract

We review theory and methodology of the class of simultaneous graphical dynamic linear models (SGDLMs) that provide flexibility, parsimony and scalability of multivariate time series analysis. Discussion includes core theoretical aspects and summaries of existing Bayesian methodology for forward filtering and forecasting with SGDLMs. The review is complemented by new theory linking dynamic graphical and factor models, and extensions of the Bayesian methodology. This addresses graphical structure uncertainty via model marginal likelihood evaluation, and analysis with missing data relevant to counterfactual analysis. The latter advances the ability to scale causal analysis to higher-dimensional time series. Aspects of the theory and methodology are exemplified in a global macroeconomic time series study with time-varying cross-series relationships and primary interests in potential causal effects. The example highlights the utility of SGDLMs with insights generated by the theoretical structure of these models, and benefits of fully Bayesian assessment of post-intervention outcomes in causal time series studies as in prediction more generally.
Paper Structure (37 sections, 24 equations, 13 figures)

This paper contains 37 sections, 24 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Graphical Model Structure
  3. Impact of Parental Specification
  4. Graph Set Intersections and Eigenstructure
  5. Sparse Factor Structure
  6. Theoretic Structure
  7. Sparse Dynamic Factor Structure
  8. Bayesian Analysis for Fitting SGDLMs
  9. SGDLM Specification: Reprise
  10. Review of Filtering and Forecasting
  11. Decoupled prior for updating at time $t$.
  12. Update to posterior and model recoupling at time $t$.
  13. Forecasting ahead at time $t$.
  14. Decoupling for evolution to time $t+1$.
  15. Marginal Likelihoods in SGDLMs
  16. ...and 22 more sections

Figures (13)

  • Figure 1: Changes in annual log GDP of $q=16$ countries. The thick line is DEU.
  • Figure 2: An example GDP simultaneous parental graph
  • Figure 3: GDP example: Sparsity pattern in ${\bm\Gamma}_t$ with OAM-based posterior means of non-zero values at $t=1990$.
  • Figure 4: Sparsity pattern of precision matrices ${\bm\Omega}_t$ implied by the GDP parental structure of Figure \ref{['fig:SGDLMgraph']}.
  • Figure 5: GDP example: Sparsity patterns and factor structure in $\mathbf{L}_t$ and $\mathbf{S}_t$ with OAM-based posterior means of non-zero values at $t=1990$.
  • ...and 8 more figures