Minimal Grid Dimensions for High-Order Connectivity via 2-Distance Dominating Sets in Spatial-Temporal Analysis

This study presents theoretical findings on the structural properties of spatial weight matrices and the minimal grid requirements for the Generalized Space-Time Autoregressive (GSTAR) model. The concept of spatial invariance is used to emphasise the second lag and the degree of spatial dependencies. The theoretical foundation for the minimal grid dimension and the requirement that each grid cell possesses at least one lag-2 neighbour is developed. Further, we establish a correlation between the minimal 2-distance dominating set in a grid and the range of lag-2 spatial regions. This correlation provides a structural comprehension of domination-based range and its impact on spatial modelling. These findings are essential for spatio-temporal analysis because they ensure robust correlation across adjacent grids and mitigate null rows in spatial weight matrices. Those factors could affect the model’s comprehension and its conclusions. These findings are evaluated with a simulation and case study of forest fires in Kalimantan Island, Indonesia. We apply the Generalized Space-Time Autoregressive model to that case with some grid configurations and evaluate them using various weight matrices. The findings indicate that a compact grid comprising 2 rows and 2 columns achieves a prediction accuracy with an error margin of under 12%. Our method for calculating connections yields results comparable to those with an error margin of approximately 11%. Based on that result, the theoretical framework demonstrates the practical importance of improving spatial-temporal modelling in real environmental scenarios.