Spatio-Temporal Autoregressions for High Dimensional Matrix-Valued Time Series

2025-08-13

AI Summary

This paper addresses the modeling challenge of high-dimensional matrix-valued time series—such as intraday trading volume curves across multiple assets—by proposing a spatiotemporal autoregressive model with dual bandwidths (STAR-Matrix), which jointly captures dynamic dependencies across assets (spatial dimension) and across time points (temporal dimension). To overcome inconsistency in conventional estimators arising from endogeneity, we develop a two-step ratio-based sequential estimation procedure that integrates the generalized method of moments framework with an iterative Yule–Walker estimator incorporating banded structural constraints. This yields consistent estimation of both spatial and temporal autoregressive coefficients. We establish root-N consistency of the estimator under high-dimensional asymptotics. Empirically, the method significantly improves forecasting accuracy and interpretability for high-frequency financial data. The proposed framework provides a scalable, identifiable, and computationally feasible paradigm for matrix-valued time series modeling.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Security and Privacy: Large-scale security measurements

Abstract

Motivated by predicting intraday trading volume curves, we consider two spatio-temporal autoregressive models for matrix time series, in which each column may represent daily trading volume curve of one asset, and each row captures synchronized 5-minute volume intervals across multiple assets. While traditional matrix time series focus mainly on temporal evolution, our approach incorporates both spatial and temporal dynamics, enabling simultaneous analysis of interactions across multiple dimensions. The inherent endogeneity in spatio-temporal autoregressive models renders ordinary least squares estimation inconsistent. To overcome this difficulty while simultaneously estimating two distinct weight matrices with banded structure, we develop an iterated generalized Yule-Walker estimator by adapting a generalized method of moments framework based on Yule-Walker equations. Moreover, unlike conventional models that employ a single bandwidth parameter, the dual-bandwidth specification in our framework requires a new two-step, ratio-based sequential estimation procedure.

Problem

• Modeling high-dimensional matrix-valued time series with spatio-temporal dynamics
• Addressing endogeneity in spatio-temporal autoregressive models estimation
• Estimating dual-bandwidth weight matrices for multi-dimensional interactions

Innovation

• Spatio-temporal autoregressive models for matrix series
• Iterated generalized Yule-Walker estimator for estimation
• Dual-bandwidth specification with ratio-based estimation