Banded Spatio-Temporal Autoregressions

TL;DR

This paper introduces a novel class of high-dimensional spatio-temporal models with banded autoregressive matrices, employing Yule-Walker equations for estimation and proposing a bandwidth selection method, with theoretical and empirical validation.

Contribution

It develops a new modeling framework for high-dimensional spatio-temporal data with banded structures, including estimation techniques and bandwidth selection, distinct from existing covariance-based methods.

Findings

The estimators are consistent and asymptotically normal.

The bandwidth selection method accurately identifies the true banded structure.

The methodology performs well on simulated and real datasets.

Abstract

We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for high-dimensional spatial panel dynamic models when panel members represent economic (or other type) individuals at many different locations. The structure is practically meaningful when the order of panel members is arranged appropriately. Note that the implied autocovariance matrices are unlikely to be banded, and therefore, the proposal is radically different from the existing literature on the inference for high-dimensional banded covariance matrices. Due to the innate endogeneity, we apply the least squares method based on a Yule-Walker equation to estimate autoregressive coefficient matrices. The estimators based on multiple Yule-Walker equations are also studied. A ratio-based method for determining the bandwidth of autoregressive matrices is also proposed. Some asymptotic properties of the inference methods are established. The proposed methodology is further illustrated using both simulated and real data sets.