Conditionally linear, matrix normal state space models

2026-09-16

AI Summary

本文开发了一类针对矩阵时间序列数据的线性状态空间模型，通过矩阵版本的卡尔曼滤波等方法估计潜在状态矩阵和参数，适用于处理混合频率、异方差性和异常值问题。

Abstract

We develop a class of linear state space models for matrix-valued time series data where the state is a latent matrix normal process. We derive matrix versions of the Kalman filter, log-likelihood, and smoother enabling estimation of the latent state matrix as well as the model's parameters. To conduct Bayesian inference, we provide algorithms that draw from the joint posterior distribution of the latent state matrices conditional on the observed data and parameters. We apply these methods to a large panel of U.S. macroeconomic time series across the 50 U.S. states. The proposed framework accommodates mixed-frequency data, heteroskedasticity, and outliers within a unified matrix-valued structure. Empirically, we find that a small number of latent factors captures the joint dynamics across states and variables, providing a parsimonious and scalable approach to modeling high-dimensional macroeconomic systems.

Problem

• matrix-valued time series
• state space models
• latent matrix normal process
• mixed-frequency data
• heteroskedasticity

Innovation

• matrix normal process
• Kalman filter
• mixed-frequency data
• latent factors