Time Series Gaussian Chain Graph Models

2026-04-09 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Research Methodology & Innovation · Depth: Expert, extended

Summary

A new class of time series Gaussian chain graph models is introduced to characterize conditional dependence structures in multivariate time series, specifically addressing variable-partitioned blockwise dependence. This model represents contemporaneous and lagged causal relations across blocks via directed edges, while capturing within-block conditional dependencies through undirected edges. In the frequency domain, this formulation leads to a cross-frequency shared group sparse plus group low-rank decomposition of inverse spectral density matrices, which is leveraged to establish identifiability. A three-stage learning procedure is proposed for estimating edge sets, involving optimizing a regularized Whittle likelihood with a group lasso penalty for sparsity and a novel tensor-unfolding nuclear norm penalty for group low-rank structure. The method's asymptotic properties ensure consistent recovery of the chain graph structure, with superior empirical performance demonstrated through simulations and an application to U.S. macroeconomic data.

Key takeaway

For AI Scientists and Research Scientists working with complex multivariate time series, this method offers a robust framework for uncovering intricate causal and conditional dependencies. You should consider applying this three-stage learning procedure, particularly its novel tensor-unfolding nuclear norm penalty, to datasets exhibiting blockwise dependence. This approach promises more accurate graph structure recovery and deeper insights into dynamic system interactions, such as monetary policy transmission mechanisms.

Key insights

A novel time series Gaussian chain graph model captures complex blockwise dependencies and causal relations using frequency-domain decomposition.

Principles

• Combine group sparsity and group low-rank structures.
• Frequency-domain analysis enables identifiability and estimation.
• Tensor-unfolding nuclear norm penalty aggregates column space information.

Method

A three-stage procedure estimates undirected edges via regularized Whittle likelihood, identifies causal ordering using conditional variance discrepancy, and estimates directed edges via multivariate time series regression and thresholding.

In practice

• Apply to U.S. macroeconomic data to analyze monetary policy.
• Extend to time series latent variable graphical models.
• Use for functional graphical models with latent functional variables.

Topics

• Time Series Chain Graphs
• Frequency Domain Modeling
• Group Sparse Low-Rank Decomposition
• Penalized Whittle Likelihood
• Causal Relation Learning

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.