Spatiotemporal Autoregressive Models for Areal Compositional Data

TL;DR

This paper develops a novel spatiotemporal autoregressive model for compositional data across regions and time, capturing complex dependencies in economic and property transaction data.

Contribution

It introduces a new multivariate autoregressive framework for composition-valued panel data, with theoretical guarantees and practical applications.

Findings

Model effectively captures spatiotemporal dependencies in compositional data.

Applications demonstrate improved understanding of economic and property market dynamics.

Framework outperforms traditional methods in case studies.

Abstract

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.