Matrix autoregressive models: generalization and Bayesian estimation

Celani Alessandro () and Pagnottoni Paolo
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Celani Alessandro: School of Statistics, University of Minnesota Twin Cities, Minneapolis, USA
Pagnottoni Paolo: School of Statistics, University of Minnesota Twin Cities, Minneapolis, USA

Studies in Nonlinear Dynamics & Econometrics, 2024, vol. 28, issue 2, 227-248

Abstract: The issue of modelling observations generated in matrix form over time is key in economics, finance and many domains of application. While it is common to model vectors of observations through standard vector time series analysis, original matrix-valued data often reflect different types of structures of time series observations which can be further exploited to model interdependencies. In this paper, we propose a novel matrix autoregressive model in a bilinear form which, while leading to a substantial dimensionality reduction and enhanced interpretability: (a) allows responses and potential covariates of interest to have different dimensions; (b) provides a suitable estimation procedure for matrix autoregression with lag structure; (c) facilitates the introduction of Bayesian estimators. We propose maximum likelihood and Bayesian estimation with Independent-Normal prior formulation, and study the theoretical properties of the estimators through simulated and real examples.

Keywords: autoregressive models; Bayesian estimation; bilinear autoregression; matrix-valued time series; multivariate time series; nearest Kronecker product projection (search for similar items in EconPapers)
JEL-codes: C11 C32 C33 C51 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1515/snde-2022-0093

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