Local Interaction Autoregressive Model for High Dimension Time Series Data

TL;DR

This paper introduces the LIAR framework for high-dimensional matrix and tensor time series forecasting, leveraging local dependencies to improve prediction accuracy and computational efficiency.

Contribution

The paper proposes a scalable LIAR model with a BIC-based neighborhood selector, providing theoretical guarantees and demonstrating superior performance over existing methods.

Findings

High success rate in neighborhood recovery

Small estimation errors achieved by LIAR

Outperforms baseline models in real TEC data

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 and study Separable LIAR, a variant with shared row and column components, for high-dimensional matrix/tensor time series forecasting problems. 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 real data applications, a Total Electron Content (TEC) case study shows the model can identify localized spatio-temporal propagation and improved prediction as compared with non-local time series prediction models.