条件线性矩阵正态状态空间模型
Conditionally linear, matrix normal state space models
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中文总结 AI 辅助
本文提出矩阵正态状态空间模型，推导矩阵卡尔曼滤波与贝叶斯推断算法，应用于美国50州宏观经济面板，以少量潜在因子实现高维系统的简约建模。
中文摘要 AI 辅助
我们开发了一类用于矩阵值时间序列数据的线性状态空间模型，其中状态是一个潜在矩阵正态过程。我们推导了卡尔曼滤波、对数似然和平滑器的矩阵版本，从而能够估计潜在状态矩阵以及模型的参数。为了进行贝叶斯推断，我们提供了在观测数据和参数条件下从潜在状态矩阵的联合后验分布中抽样的算法。我们将这些方法应用于涵盖美国50个州的大型美国宏观经济时间序列面板。所提出的框架在统一的矩阵值结构内适应混合频率数据、异方差性和异常值。实证上，我们发现少量潜在因子能够捕捉跨州和变量的联合动态，为建模高维宏观经济系统提供了一种简约且可扩展的方法。
英文摘要
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.
发表机构
- University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
- Pontifical Catholic University of Rio de Janeiro（里约热内卢天主教大学）
机构由 AI 辅助整理，请以论文原文为准。
