Drew D. Creal, Marcelo C. Medeiros, Rodrigo Sarlo
arXiv 16 Sep 2026 · Econometrics
arXiv:2609.18734 · PDF · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Doucet, Arnaud, and Christophe Andrieu (2001) Iterative algorithms for state estimation of jump Markov linear systems, IEEE Transactions on Signal Processing\/ 49, 1216–1227 | 0.737 | 3 | 2 | 100% |
| 2 | Durbin, James, and Siem Jan Koopman (2002) A simple and efficient simulation smoother for state space time series analysis., Biometrika\/ 89, 603–616 | 0.737 | 3 | 2 | 100% |
| 3 | Gerlach, Richard H, Christopher K. Carter, and Robert Kohn (2000) Efficient Bayesian inference for dynamic mixture models., Journal of the American Statistical Association\/ 95, 819–828 | 0.737 | 3 | 2 | 100% |
| 4 | Jungbacker, Borus, and Siem Jan Koopman (2015) Likelihood-based dynamic factor analysis for measurement and forecasting., The Econometrics Journal\/ 18, C1–C21 | 0.737 | 3 | 2 | 100% |
| 5 | Chan, Joshua C. C., and Ivan Jeliazkov (2009) Efficient simulation and integrated likelihood estimation in state space models, International Journal of Mathematical Modelling… | 0.644 | 2 | 2 | 100% |
| 6 | Durbin, James, and Siem Jan Koopman (2012) Time Series Analysis by State Space Methods\/, second edition (Oxford University Press, Oxford, UK) | 0.644 | 2 | 2 | 100% |
| 7 | Mariano, Roberto S., and Yasutomo Murasawa (2003) A new coincident index of business cycles based on monthly and quarterly series, Journal of Applied Econometrics\/ 18, 427–443 | 0.644 | 2 | 2 | 100% |
| 8 | de Jong, Piet (1991) The diffuse Kalman filter, The Annals of Statistics\/ 19, 1073–83 | 0.644 | 2 | 2 | 100% |
| 9 | de Jong, Piet, and Neil Shephard (1995) The simulation smoother for time series models, Biometrika\/ 82, 339–350 | 0.644 | 2 | 2 | 100% |
| 10 | Carvalho, Carlos M., and Mike West (2007) Dynamic matrix-variate graphical models, Bayesian Analysis\/ 2, 69–97 | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 47 scored citations.