Estimation of the spatial weighting matrix for regular lattice data -- An adaptive lasso approach with cross-sectional resampling

Spatial econometric research typically relies on the assumption that the spatial dependence structure is known in advance and is represented by a deterministic spatial weights matrix. Contrary to classical approaches, we investigate the estimation of sparse spatial dependence structures for regular lattice data. In particular, an adaptive least absolute shrinkage and selection operator (lasso) is used to select and estimate the individual connections of the spatial weights matrix. To recover the spatial dependence structure, we propose cross-sectional resampling, assuming that the random process is exchangeable. The estimation procedure is based on a two-step approach to circumvent simultaneity issues that typically arise from endogenous spatial autoregressive dependencies. The two-step adaptive lasso approach with cross-sectional resampling is verified using Monte Carlo simulations. Eventually, we apply the procedure to model nitrogen dioxide ($\mathrm{NO_2}$) concentrations and show that estimating the spatial dependence structure contrary to using prespecified weights matrices improves the prediction accuracy considerably

Estimation of the spatial weighting matrix for regular lattice data—An adaptive lasso approach with cross-sectional resampling

Spatial autoregressive models typically rely on the assumption that the spatial dependence structure is known in advance and is represented by a deterministic spatial weights matrix, although it is unknown in most empirical applications. Thus, we investigate the estimation of sparse spatial dependence structures for regular lattice data. In particular, an adaptive least absolute shrinkage and selection operator (lasso) is used to select and estimate the individual nonzero connections of the spatial weights matrix. To recover the spatial dependence structure, we propose cross-sectional resampling, assuming that the random process is exchangeable. The estimation procedure is based on a two-step approach to circumvent simultaneity issues that typically arise from endogenous spatial autoregressive dependencies. The two-step adaptive lasso approach with cross-sectional resampling is verified using Monte Carlo simulations. Eventually, we apply the procedure to model nitrogen dioxide (Formula presented.) concentrations and show that estimating the spatial dependence structure contrary to using prespecified weights matrices improves the prediction accuracy considerably. © 2021 The Authors. Environmetrics published by John Wiley & Sons, Ltd

Estimation of Asymmetric Spatial Autoregressive Dependence on Irregular Lattices

In spatial econometrics, we usually assume that the spatial dependence structure is known and that all information about it is contained in a spatial weights matrix W. However, in practice, the structure of W is unknown a priori and difficult to obtain, especially for asymmetric dependence. In this paper, we propose a data-driven method to obtain W, whether it is symmetric or asymmetric. This is achieved by calculating the area overlap of the adjacent regions/districts with a given shape (a pizza-like shape, in our case). With W determined in this way, we estimate the potentially asymmetric spatial autoregressive dependence on irregular lattices. We verify our method using Monte Carlo simulations for finite samples and compare it with classical approaches such as Queen’s contiguity matrices and inverse-distance weighting matrices. Finally, our method is applied to model the evolution of sales prices for building land in Brandenburg, Germany. We show that the price evolution and its spatial dependence are mainly driven by the orientation towards Berlin

Estimation of Anisotropic, Time‐Varying Spatial Spillovers of Fine Particulate Matter Due to Wind Direction

This paper investigates the effect of daily wind direction and speed on the spatio-temporal distribution of particulate matter, PM2.5. Interdependencies between the PM2.5 values of different monitoring sites are characterized by incorporating time-varying anisotropic spatial weighting matrices. These weights are parameterized with respect to wind direction, speed and a range that marks the bandwidth of admissible deviations between wind direction and bearing. The empirical analysis is based on daily PM2.5 values recorded by monitoring sites located across the eastern United States in 2015 as well as several meteorological regressors. More precisely, we propose a space-time dynamic panel data model with different spatial autoregressive, temporal and exogenous dependencies. All model parameters are estimated by the quasi-maximum likelihood approach. The estimation procedure, including the identification of the range and spatial parameters, is verified by Monte Carlo simulations. We show that part of the spatial dependency of PM2.5 values is explained by wind direction

Spatial statistics, or how to extract knowledge from data

In this paper, we give an overview of selected statistical models to draw (statistically significant) conclusions from data. This is particularly important to prove theoretical/physical models. For this reason, we initially describe classical modeling approaches in geostatistics and spatial econometrics. Moreover, we show how large spatial and spatiotemporal data can be modeled by these approaches. Therefore, we sketch selected suitable methods and their computational implementation. Thus, the paper should give a general guideline to analyze big geospatial data, where “big data” refers to the total number of spatially dependent observations, and to draw conclusions from these data. Finally, we compare two of these approaches by applying them to an empirical data set. To be precise, we model the particulate matter concentration (PM2.5) in Colorado