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.

摘要

在本文中，我们提出了一种两阶段 LASSO 估计方法，用于估计时空自回归模型的完整空间权重矩阵。此外，我们允许每个空间位置的局部均值存在未知数量的结构断裂。然而，这些局部变化的平均水平很容易被误认为是空间依赖性，反之亦然。因此，所提出的方法联合估计空间依赖性、所有结构断裂和局部平均水平。对于惩罚参数的选择，我们基于经验空间自相关与模型中估计的空间依赖性之间的距离提出了一种全新的选择标准。通过模拟研究，我们将展示估计器的有限样本性能，并就何时应用该方法提供实用指导。最后，将通过 1995 年至 2014 年间柏林同城每月房地产价格的实证示例来说明该方法。空间单位将由各自的邮政编码定义。新方法使我们能够估计当地平均水平，并量化由于空间溢出效应而观察到的价格与这些水平的偏差。这样做时，整个空间依赖结构是在数据驱动的基础上估计的。本文的补充材料可在线获取。新方法使我们能够估计当地平均水平，并量化由于空间溢出效应而观察到的价格与这些水平的偏差。这样做时，整个空间依赖结构是在数据驱动的基础上估计的。本文的补充材料可在线获取。新方法使我们能够估计当地平均水平，并量化由于空间溢出效应而观察到的价格与这些水平的偏差。这样做时，整个空间依赖结构是在数据驱动的基础上估计的。本文的补充材料可在线获取。