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

TL;DR

This paper introduces novel spatio-temporal autoregressive models for high-dimensional matrix-valued time series, capturing interactions across assets and time, with a new estimation method addressing endogeneity and dual-bandwidth complexity.

Contribution

It develops a new class of models incorporating spatial and temporal dynamics in matrix time series, along with an iterated generalized Yule-Walker estimator for consistent parameter estimation.

Findings

Effective modeling of intraday trading volume curves across assets.

Consistent estimation of dual-bandwidth parameters.

Enhanced understanding of cross-asset and temporal interactions.

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.