Comparing Areal and Grid Supports for Fire Radiative Power within a GSTAR (p; λ₁, λ₂, …, λₚ) Framework - Zuleha, Zuleha; Huda, Nur'ainul Miftahul; Imro'ah, Nurfitri (JTAM (Jurnal Teori dan Aplikasi Matematika), 2026)
Forest fire phenomena exhibit spatial interdependence and temporal dependence, necessitating a spatiotemporal modeling approach to capture the dynamics of fire occurrences. This study models and predicts forest fires using Fire Radiative Power (FRP) as an indicator of fire intensity. Weekly hotspot data from NASA FIRMS, covering the period from July 2024 to August 2025, were analyzed using the Generalized Space-Time Autoregressive (GSTAR) model. The modeling was conducted by considering various forms of spatial partitioning and spatial weight matrices to capture inter-location dependencies. Four spatial partitioning schemes were employed: areal, and grids of 0.50°×0.50°, 1.00°×1.00°, and 1.25°×1.25°; alongside three spatial weight matrices: Queen Contiguity, Rook Contiguity, and Inverse Distance Weighting (IDW). The temporal order and spatial lag were determined using STACF and STPACF plots. From these combinations, 42 GSTAR models were constructed and evaluated through a three-stage process of estimation and residual diagnostic testing. The results indicate that the GSTAR (1;1) model with a 1.00°×1.00° grid and Rook Contiguity and IDW spatial weight matrices is the best-performing model. This model satisfies the white noise assumption and yields a Root Mean Square Error (RMSE) of 6.866, which is the smallest among all evaluated models. The estimates indicate that fires at a given location are influenced by prior conditions and spatial interactions with surrounding areas, suggesting that the GSTAR model supports spatiotemporal monitoring and early warning systems.