Estimation of the Spatial Weighting Matrix for Spatiotemporal Data under the Presence of Structural Breaks

TL;DR

This paper introduces a two-step lasso method to estimate spatial weights matrices in spatiotemporal models, accounting for structural breaks and local mean shifts, demonstrated through real estate data analysis.

Contribution

It presents a novel convex optimization approach for jointly estimating spatial dependence, structural breaks, and local means in spatiotemporal data.

Findings

Effective estimation of spatial weights matrices demonstrated in simulations

Method successfully identifies structural breaks in real estate prices

Quantifies spatial spill-over effects in regional price data

Abstract

In this paper, we propose a two-step lasso estimation approach to estimate the full spatial weights matrix of spatiotemporal autoregressive models. In addition, we allow for an unknown number of structural breaks in the local means of each spatial locations. The proposed approach jointly estimates the spatial dependence, all structural breaks, and the local mean levels. In addition, it is easy to compute the suggested estimators, because of a convex objective function resulting from a slight simplification. Via simulation studies, we show the finite-sample performance of the estimators and provide a practical guidance, when the approach could be applied. Eventually, the invented method is illustrated by an empirical example of regional monthly real-estate prices in Berlin from 1995 to 2014. The spatial units are defined by the respective ZIP codes. In particular, we can estimate local mean levels and quantify the deviation of the observed prices from these levels due to spatial spill over effects.