Compositional data, such as regional shares of economic sectors or property transactions, are central to understanding structural change in economic systems across space and time. This paper introduces a spatiotemporal multivariate autoregressive model tailored for panel data with composition-valued responses at each areal unit and time point. The proposed framework enables the joint modelling of temporal dynamics and spatial dependence under compositional constraints, and is estimated via a quasi-maximum likelihood approach. We build on recent theoretical advances to establish the identifiability and asymptotic properties of the estimator as both the number of regions and the number of time points grow. The utility and flexibility of the model are demonstrated through two applications: analysing property transaction compositions in an intra-city housing market (Berlin), and regional sectoral compositions in Spain's economy. These case studies highlight how the proposed framework captures key features of spatiotemporal economic processes that are often missed by conventional methods.

翻译：成分数据，如经济部门的区域份额或房地产交易构成，对于理解经济系统在空间和时间上的结构变化至关重要。本文提出了一种时空多元自回归模型，专门用于处理每个区域单元和时间点上具有成分值响应的面板数据。所提出的框架能够在成分约束下联合建模时间动态和空间依赖性，并通过拟极大似然方法进行估计。我们基于最新的理论进展，建立了在区域数量和时间点数量同时增长时估计量的可识别性和渐近性质。通过两个应用案例展示了模型的实用性和灵活性：分析城市内部住房市场（柏林）的房地产交易构成，以及西班牙经济的区域部门构成。这些案例研究突显了所提出的框架如何捕捉时空经济过程的关键特征，而这些特征往往被传统方法所忽略。