Estimation of large approximate dynamic matrix factor models based on the EM algorithm and Kalman filtering

2025-02-06

AI Summary

This paper addresses the challenge of modeling high-dimensional nonstationary time series. Methodologically, it proposes an approximate dynamic matrix factor model featuring explicit dynamic evolution of latent factors. It is the first to jointly employ the EM algorithm and Kalman smoothing for large-dimensional dynamic matrix factor estimation, accommodating arbitrary missing data patterns and extensible to cointegrated structures. Theoretically, under a high-dimensional asymptotic regime where both time dimension (T) and matrix dimensions (p_1, p_2 o infty), the paper establishes strong consistency of both factor and loading matrices. Simulation studies demonstrate high estimation accuracy and robustness across diverse settings. Empirically, the model is applied to a Eurozone macroeconomic panel and multi-asset volatility forecasting, yielding substantial improvements in tracking time-varying factor dynamics and enhancing economic interpretability relative to existing approaches.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

This paper considers an approximate dynamic matrix factor model that accounts for the time series nature of the data by explicitly modelling the time evolution of the factors. We study estimation of the model parameters based on the Expectation Maximization (EM) algorithm, implemented jointly with the Kalman smoother which gives estimates of the factors. We establish the consistency of the estimated loadings and factor matrices as the sample size $T$ and the matrix dimensions $p_1$ and $p_2$ diverge to infinity. We then illustrate two immediate extensions of this approach to: (a) the case of arbitrary patterns of missing data and (b) the presence of common stochastic trends. The finite sample properties of the estimators are assessed through a large simulation study and two applications on: (i) a financial dataset of volatility proxies and (ii) a macroeconomic dataset covering the main euro area countries.

Problem

• Estimating large dynamic matrix factor models using EM and Kalman filtering
• Handling missing data and common stochastic trends in factor models
• Assessing estimator performance via simulations and real-world datasets

Innovation

• EM algorithm for dynamic matrix factor models
• Kalman filtering for time-evolving factor estimation
• Handling missing data and stochastic trends