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

ABSTRACT

In this article, we propose a two-stage LASSO estimation approach for the estimation of a full spatial weight matrix of spatiotemporal autoregressive models. In addition, we allow for an unknown number of structural breaks in the local means of each spatial location. These locally varying mean levels, however, can easily be mistaken as spatial dependence and vice versa. Thus, the proposed approach jointly estimates the spatial dependence, all structural breaks, and the local mean levels. For selection of the penalty parameter, we propose a completely new selection criterion based on the distance between the empirical spatial autocorrelation and the spatial dependence estimated in the model. Through simulation studies, we will show the finite-sample performance of the estimators and provide practical guidance as to when the approach could be applied. Finally, the method will be illustrated by an empirical example of intra-city monthly real-estate prices in Berlin between 1995 and 2014. The spatial units will be defined by the respective postal codes. The new approach allows us to estimate local mean levels and quantify the deviation of the observed prices from these levels due to spatial spillover effects. In doing so, the entire spatial dependence structure is estimated on a data-driven basis. Supplementary materials for this article are available online.

KEYWORDS:

• LASSO estimation
• Real-estate market
• Spatial weight matrix
• Spatiotemporal autoregressive models
• Statistical learning
• Structural breaks

Supplementary Materials

All source code and data to reproduce the empirical results are provided in the supplementary materials.

Acknowledgments

We want to thank the two anonymous reviewers of JCGS whose suggestions and comments helped us a lot in the revision process. We would also like to thank the Associate Editor for his detailed and thorough comments.