# Sparsity-Induced Global Matrix Autoregressive Model with Auxiliary Network Data

arXiv: https://arxiv.org/abs/2503.08579 · HTML: https://mlsanity.com/paper/2503.08579/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 22 of 22)

- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Factor Models for High-Dimensional Tensor Time Series](https://mlsanity.com/paper/1905.07530/) (2019)
- [Autoregressive Models for Matrix-Valued Time Series](https://mlsanity.com/paper/1812.08916/) (2018)
- [High-dimensional vector autoregressive time series modeling via tensor decomposition](https://mlsanity.com/paper/1909.06624/) (2019)
- [Constrained Factor Models for High-Dimensional Matrix-Variate Time Series](https://mlsanity.com/paper/1710.06075/) (2017)
- [Statistical Inference for High-Dimensional Matrix-Variate Factor Model](https://mlsanity.com/paper/2001.01890/) (2020)
- [Factor Models for Matrix-Valued High-Dimensional Time Series](https://mlsanity.com/paper/1610.01889/) (2016)
- [High Dimensional and Banded Vector Autoregressions](https://mlsanity.com/paper/1502.07831/) (2015)
- [High-Dimensional Low-Rank Tensor Autoregressive Time Series Modeling](https://mlsanity.com/paper/2101.04276/) (2021)
- [Modelling matrix time series via a tensor CP-decomposition](https://mlsanity.com/paper/2112.15423/) (2021)
- [Community Network Auto-Regression for High-Dimensional Time Series](https://mlsanity.com/paper/2007.05521/) (2020)
- [Multi-linear Tensor Autoregressive Models](https://mlsanity.com/paper/2110.00928/) (2021)
- [Banded Spatio-Temporal Autoregressions](https://mlsanity.com/paper/1803.01699/) (2018)
- [KoPA: Automated Kronecker Product Approximation](https://mlsanity.com/paper/1912.02392/) (2019)
- [Generalized Yule-Walker Estimation for Spatio-Temporal Models with Unknown Diagonal Coefficients](https://mlsanity.com/paper/1505.01177/) (2015)
- [A Two-Way Transformed Factor Model for Matrix-Variate Time Series](https://mlsanity.com/paper/2011.09029/) (2020)
- [Simultaneous Estimation and Group Identification for Network Vector Autoregressive Model with Heterogeneous Nodes](https://mlsanity.com/paper/2209.12229/) (2022)
- [One-way or Two-way Factor Model for Matrix Sequences?](https://mlsanity.com/paper/2110.01008/) (2021)
- [Matrix Factor Analysis: From Least Squares to Iterative Projection](https://mlsanity.com/paper/2112.04186/) (2021)
- [Mixture Matrix-valued Autoregressive Model](https://mlsanity.com/paper/2312.06098/) (2023)
- [Multi-relational Network Autoregression Model with Latent Group Structures](https://mlsanity.com/paper/2406.03296/) (2024)

## Abstract (arXiv)

Jointly modeling and forecasting economic and financial variables across a large set of countries has long been a significant challenge. Two primary approaches have been utilized to address this issue: the vector autoregressive model with exogenous variables (VARX) and the matrix autoregression (MAR). The VARX model captures domestic dependencies, but treats variables exogenous to represent global factors driven by international trade. In contrast, the MAR model simultaneously considers variables from multiple countries but ignores the trade network. In this paper, we propose an extension of the MAR model that achieves these two aims at once, i.e., studying both international dependencies and the impact of the trade network on the global economy. Additionally, we introduce a sparse component to the model to differentiate between systematic and idiosyncratic cross-predictability. To estimate the model parameters, we propose both a likelihood estimation method and a bias-corrected alternating minimization version. We provide theoretical and empirical analyses of the model's properties, alongside presenting intriguing economic insights derived from our findings.