High-Dimensional Regularized Additive Matrix Autoregressive Model

TL;DR

This paper introduces a regularized additive matrix autoregressive model for high-dimensional time series that improves interpretability and computational efficiency by leveraging low-rank and sparse structures, with proven theoretical guarantees.

Contribution

It proposes a novel convex additive matrix autoregressive model with low-rank plus sparse transition matrices, addressing interpretability and computational challenges in high-dimensional settings.

Findings

Model demonstrates superior interpretability over bilinear and Tucker models.

Algorithm achieves scalable and efficient estimation in high dimensions.

Theoretical error bounds validate model performance.

Abstract

High-dimensional time series has diverse applications in econometrics and finance. Recent models for capturing temporal dependence have employed a bilinear representation for matrix time series, or the Tucker-decomposition based representation in case of tensor time series. A bilinear or Tucker-decomposition based temporal effect is difficult to interpret on many occasions, along with its computational complexity due to the non-convex nature of the underlying optimization problem. Moreover, the existing matrix case models have not sufficiently explored the possibilities of imposing any lower-dimensional pattern on the transition matrices. In this work, we propose a regularized additive matrix autoregressive model with additive interaction of row-wise and column-wise temporal dependence, that offers more interpretability, less computational burden due to its convex nature and estimation of the underlying low rank plus sparse pattern of its transition matrices. We address the issue of identifiability of the various components in our model and subsequently develop a scalable Alternating Block Minimization algorithm for estimating the parameters. We provide a finite sample error bound under high-dimensional scaling for the model parameters. Finally, the efficacy of the proposed model is demonstrated on synthetic and real data.