Structural Identification for Spatio-Temporal Dynamic Models

Identifying latent cluster structures in spatial trends constitutes an important yet challenging task in diverse applications. In this paper, we propose a novel method based on a discrepancy measure over small spatial blocks that effectively uncovers heterogeneity within dynamic spatial data. Our approach effectively detects boundaries where structural changes occur, thus allowing for more nuanced insights into underlying spatial patterns. Unlike methods predicated on strong stationarity assumptions, our framework accommodates piecewise-defined parameters and irregular sampling locations, enabling its broad applicability to real-world datasets. We further establish asymptotic properties and limit distributions of the proposed methods by leveraging the notion of spatial physical dependence, accounting for correlations across spatial domains. Simulations and real data analyses confirm the effectiveness of the method, highlighting its robustness and accuracy in identifying complex spatio-temporal structures.