Conference Agenda

We consider a structural matrix-autregressive (SMAR) model to conduct impulse response analysis for structural shocks to matrix-valued time series. The MAR model of order $p$ offers a parsimonious and interpretable framework for these time series, thus addressing issues of high-dimensionality in corresponding vector-autoregressive (VAR) models. To interpret the dynamics, we resort to impulse response analysis as a popular tool from the SVAR context. Its conclusions rely on the valid identification of structural shocks that are mutually contemporaneously uncorrelated and interpretable. In contrast to the existing literature, the proposed SMAR model enables the identification of multiple structural shocks. To address the restrictive nature of the single-term MAR($p$) model, we discuss the extension to a multi-term SMAR($p$) model as a compromise between the single-term SMAR and the (unrestricted) SVAR model, trading off parsimony against flexibility. We discuss its identification, focusing in particular on issues that arise due to the typical Kronecker-product structure of the coefficient matrices in the MAR framework. Further, we discuss estimation and inference in the general multi-term SMAR($p$) model, including a bootstrap method to compute confidence bands for the impulse response curves. In this context, a key point concerns model misspecification and the use of MAR models to approximate more general SVAR data generating processes. Finally, we demonstrate the performance and practical use of our approach by Monte Carlo simulations and a real data application.