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[https://www.tandfonline.com/loi/ucgs20](https://www.tandfonline.com/loi/ucgs20)  \nEstimation of the Spatial Weighting Matrix for Spatiotemporal Data under the Presence of Structural Breaks  \nPhilipp Otto & Rick Steinert  \nTo cite this article: Philipp Otto & Rick Steinert (2022): Estimation of the Spatial Weighting Matrix for Spatiotemporal Data under the Presence of Structural Breaks, Journal of Computational and Graphical Statistics, DOI: 10. 1080/10618600 .2022.2107530  \nTo link to this article: [https://doi.org/10.1080/10618600.2022.2107530](https://doi.org/10.1080/10618600.2022.2107530)  \n View supplementary material   \n\n|  Published online: 04 Oct 2022. |  |\n| --- | --- |\n|  Submit your article to this journal  |  |\n|  Article views: 142 |  |\n| | View related articles  |\n| | View Crossmark data |\n|  Citing articles: 1 View citing articles  |  |\n\nFull Terms & Conditions of access and use can be found at [https://www.tandfonline.com/action/journalInformation?journalCode=ucgs20](https://www.tandfonline.com/action/journalInformation?journalCode=ucgs20)  \nJOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2022, VOL. 00, NO. 0,1–16  \n[https://doi.org/10.1080/10618600.2022.2107530](https://doi.org/10.1080/10618600.2022.2107530)  \nEstimation of the Spatial Weighting Matrix for Spatiotemporal Data under the Presence of Structural Breaks  \nPhilipp Ottoa  and Rick Steinertb   \na Leibniz University Hannover, Hannover, Germany; b European University Viadrina, Frankfurt (Oder), Germany  \nABSTRACT  \nIn this article, we propose a two-stage LASSO estimation approach for the estimation of a full spatial weight matrix ofspatiotemporal 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.  \nARTICLE HISTORY  \nReceived June 2019  \nAccepted July 2022  \nKEYWORDS  \nLASSO estimation;  \nReal-estate market; Spatial weight matrix; Spatiotemporal autoregressive models; Statistical learning; Structural breaks  \n1. Introduction  \nSpatial autoregressive models, along with conditional autoregressive models, require a definition of a suitable spatial dependence structure via the so-called spatial weights matrix (see e.g., Pace and LeSage 2009; Elhorst 2010; Ver Hoef, Hanks, and Hooten 2018) . This matrix, like an adjacency matrix in graphical models, defines how the locations are connected, thereby defining which locations have a possibility of being dependent, along with to what extent. The spatial autoregressive term is then classically modeled as a multiple of the product of this predefined weighting matrix and the vector of observations. Indeed, this also means that estimated spatial autoregressive coefficient depends on the choice of this matrix. Thus, all coefficients, as well as inference o","cbCailr2KmEDFXcf","https://ap.wps.com/l/cbCailr2KmEDFXcf","pdf",2773862,17,"English","# Abstract\n## 1. Introduction\n## Article Information\n## Keywords","[{\"question\":\"What estimation approach is proposed for the spatial weighting matrix?\",\"answer\":\"A two-stage LASSO estimation approach is proposed to estimate a full spatial weight matrix for spatiotemporal autoregressive models.\"},{\"question\":\"How does the method handle structural breaks?\",\"answer\":\"It allows an unknown number of structural breaks in the local means for each spatial location and jointly estimates these breaks with spatial dependence.\"},{\"question\":\"How is the penalty parameter selected?\",\"answer\":\"A new selection criterion is introduced based on the distance between empirical spatial autocorrelation and the spatial dependence estimated in the model.\"}]","Estimation of the Spatial Weighting Matrix for Spatiotemporal Data under the Presence of Structural Breaks | PDF",1792616793,43]