Bayesian Dynamic Factor Models for High-dimensional Matrix-valued Time Series

TL;DR

This paper develops Bayesian matrix dynamic factor models for high-dimensional time series data, allowing for time-varying volatility, outliers, and cross-sectional correlation, with methods for model selection and validation.

Contribution

It introduces a novel Bayesian framework for matrix-valued time series that includes model comparison techniques and demonstrates effectiveness through simulations and real data applications.

Findings

Accurate factor estimation demonstrated in Monte Carlo experiments.

Effective model selection via marginal likelihood and cross-entropy method.

Successful application to macroeconomic and financial datasets.

Abstract

We introduce a class of Bayesian matrix dynamic factor models that accommodates time-varying volatility, outliers, and cross-sectional correlation in the idiosyncratic components. For model comparison, we employ an importance-sampling estimator of the marginal likelihood based on the cross-entropy method to determine: (1) the optimal dimension of the factor matrix; (2) whether a vector- or matrix-valued structure is more suitable; and (3) whether an approximate or exact factor model is favored by the data. Through a series of Monte Carlo experiments, we demonstrate the accuracy of the factor estimates and the effectiveness of the marginal likelihood estimator in correctly identifying the true model. Applications to macroeconomic and financial datasets illustrate the model's ability to capture key features in matrix-valued time series.