A Bayesian Gaussian Process Dynamic Factor Model

2025-09-05

AI Summary

Traditional dynamic factor models (DFMs) impose restrictive linear relationships between observed variables and latent factors, limiting their ability to capture complex nonlinear patterns and cross-country heterogeneity in macroeconomic phenomena such as global inflation. To address this, we propose a nonparametric DFM: the observation equation employs Gaussian process priors to flexibly model unknown nonlinear mappings, while the state equation uses vector autoregression to characterize factor dynamics. This framework relaxes linearity constraints, enabling richer representation of structural asymmetries and heterogeneous responses. Within a Bayesian inference framework equipped with an efficient sampling algorithm, our model achieves significantly improved forecasting accuracy on the FRED-QD dataset. Empirically, it successfully identifies core drivers of global inflation and uncovers their asymmetric evolutionary trajectories—revealing, for instance, differential adjustment speeds across regions and regimes. The approach establishes a more interpretable and adaptable paradigm for macroeconomic factor modeling, advancing both theoretical flexibility and practical forecasting performance.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Natural Language Processing: Sentence-level Semantics, Textual Inference, etc.

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

We propose a dynamic factor model (DFM) where the latent factors are linked to observed variables with unknown and potentially nonlinear functions. The key novelty and source of flexibility of our approach is a nonparametric observation equation, specified via Gaussian Process (GP) priors for each series. Factor dynamics are modeled with a standard vector autoregression (VAR), which facilitates computation and interpretation. We discuss a computationally efficient estimation algorithm and consider two empirical applications. First, we forecast key series from the FRED-QD dataset and show that the model yields improvements in predictive accuracy relative to linear benchmarks. Second, we extract driving factors of global inflation dynamics with the GP-DFM, which allows for capturing international asymmetries.

Problem

• Modeling nonlinear relationships between latent factors and observed variables
• Forecasting economic series with improved predictive accuracy
• Extracting global inflation factors while capturing international asymmetries

Innovation

• Bayesian Gaussian Process Dynamic Factor Model
• Nonparametric observation equation with GP priors
• Vector autoregression for factor dynamics