Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach

TL;DR

This paper introduces reduced-rank tensor regression models for matrix-valued time series, enabling better understanding of co-movements across different dimensions and linking them to existing models, with applications to economic data.

Contribution

It develops a novel tensor-based reduced-rank regression framework for matrix time series, connecting co-movement structures to established models and demonstrating practical utility.

Findings

Identifies co-movements in economic time series across regions and indicators.

Links tensor regression structures to serial correlation and index models.

Provides empirical insights into economic co-movement patterns.

Abstract

Reduced-rank regressions are powerful tools used to identify co-movements within economic time series. However, this task becomes challenging when we observe matrix-valued time series, where each dimension may have a different co-movement structure. We propose reduced-rank regressions with a tensor structure for the coefficient matrix to provide new insights into co-movements within and between the dimensions of matrix-valued time series. Moreover, we relate the co-movement structures to two commonly used reduced-rank models, namely the serial correlation common feature and the index model. Two empirical applications involving U.S.\ states and economic indicators for the Eurozone and North American countries illustrate how our new tools identify co-movements.