Sparse Generalized Yule-Walker Estimation for Large Spatio-temporal Autoregressions with an Application to NO2 Satellite Data

TL;DR

This paper introduces a data-driven, sparse estimation method for high-dimensional spatio-temporal autoregressive models that infers spatial interactions directly from data, with applications to satellite NO2 data and improved forecasting.

Contribution

It proposes a novel penalized Yule-Walker approach for estimating sparse spatial and temporal dependencies without predefined spatial matrices, including customized shrinkage for spatial grid data.

Findings

Strong finite sample performance demonstrated in simulations

Improved forecast accuracy for NO2 satellite data

Evidence of significant spatial interactions in empirical application

Abstract

We consider a high-dimensional model in which variables are observed over time and space. The model consists of a spatio-temporal regression containing a time lag and a spatial lag of the dependent variable. Unlike classical spatial autoregressive models, we do not rely on a predetermined spatial interaction matrix, but infer all spatial interactions from the data. Assuming sparsity, we estimate the spatial and temporal dependence fully data-driven by penalizing a set of Yule-Walker equations. This regularization can be left unstructured, but we also propose customized shrinkage procedures when observations originate from spatial grids (e.g. satellite images). Finite sample error bounds are derived and estimation consistency is established in an asymptotic framework wherein the sample size and the number of spatial units diverge jointly. Exogenous variables can be included as well. A simulation exercise shows strong finite sample performance compared to competing procedures. As an empirical application, we model satellite measured NO2 concentrations in London. Our approach delivers forecast improvements over a competitive benchmark and we discover evidence for strong spatial interactions.