Abstract

High-dimensional matrix and tensor time series often exhibit local dependency,

where each entry interacts mainly with a small neighborhood.

Accounting for local interactions in a prediction model can greatly reduce the dimensionality of the parameter

space, leading to more efficient inference and more accurate predictions. We propose a Local

Interaction Autoregressive (LIAR) framework for high-dimensional matrix and tensor time

series forecasting problems, and study Separable LIAR, a matrix variant with shared row

and column components. We derive a scalable parameter estimation algorithm via parallel

least squares with a BIC-type neighborhood selector. Theoretically, we show consistency of

neighborhood selection and derive error bounds for kernel and auto-covariance estimation.

Numerical simulations show that the BIC selector recovers the true neighborhood with high

success rates, the LIAR achieves small estimation errors, and the forecasts outperform matrix

time-series baselines. In a Total Electron Content (TEC) application, the proposed method

identifies localized spatio-temporal propagation patterns and achieves improved prediction

compared with non-local time series prediction models.

Key words and phrases: Autoregressive model; Matrix time series; Tensor time series; Local interaction; Neighborhood selection; Total Electron Content

Information

Preprint No.SS-2025-0419
Manuscript IDSS-2025-0419
Complete AuthorsJingyang Li, Yang Chen
Corresponding AuthorsJingyang Li
Emailsjjyyli@fudan.edu.cn

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Acknowledgments

We thank Hu Sun (University of Michigan, Ph.D. 2024) and Professor Han Xiao

(Rutgers University) for discussions on the matrix autoregressive model with banded

structures. YC acknowledges support from NSF AGS Award 2419187, NASA Federal

Award No. 80NSSC23M0192, and No. 80NSSC23M0191.