Robust Estimation for Dynamic Spatial Autoregression Models with Nearly Optimal Rates

Abstract

Spatial autoregression has been extensively studied in various applications, yet its robust estimation methods have received limited attention. In this work, we introduce two dynamic spatial autoregression (DSAR) models aimed at capturing temporal trends and depicting the asymmetric network effects of the units. For both DSAR models, we propose a truncated Yule-Walker estimation method, which is tailored to achieve robust estimation in the presence of heavy-tailed data. Additionally, we extend the robust estimation procedure to a constraint estimation framework using the Dantzig selector, which is able to discover sparse network effects observed in real-world applications. Theoretically, the minimax optimality of proposed estimators is derived under certain conditions on the weighting matrix. Empirical studies on financial contagion in the Chinese stock market and analysis of live streaming popularity, are conducted to validate the efficacy of the proposed estimation methods.

Keywords: Dynamic spatial autoregression, Network data, Robust estimation, Truncation method, Minimax optimality.