Regional compositional trajectories and structural change: A spatiotemporal multivariate autoregressive framework

2025-07-18

AI Summary

This paper addresses the modeling challenge of spatiotemporal panel data with compositional structure—such as sectoral shares or transaction proportions—in regional economic systems. We propose a novel spatiotemporal multivariate autoregressive model that jointly incorporates compositional constraints, spatial dependence, and multi-period dynamics within a unified framework, ensuring parameter identifiability. Under a double-asymptotic regime (both cross-sectional units and time periods grow), we establish rigorous statistical inference theory. The model employs quasi-maximum likelihood estimation, integrating spatial lag and vector autoregression techniques to handle high-dimensional compositional response variables effectively. Empirical applications to Berlin housing transaction data and Spanish regional economic structure data demonstrate that the model captures structural spatiotemporal evolution patterns overlooked by conventional methods, thereby enhancing both the accuracy and interpretability of regional economic dynamic modeling.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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 identifiability and asymptotic properties of the estimator when both the number of regions and 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.

Problem

• Modeling spatiotemporal compositional economic data dynamics
• Estimating spatial-temporal dependencies under compositional constraints
• Analyzing regional economic structural changes with novel framework

Innovation

• Spatiotemporal multivariate autoregressive model for compositions
• Quasi maximum likelihood estimation under constraints
• Joint modelling of temporal and spatial dependencies