New algorithm in detecting outliers from a spatial-temporal perspective in forest fire cases

Spatial-temporal outlier detection is frequently carried out using model-free, spatial-only methods (e.g., Local Moran's I) that disregard temporal dependencies, or through univariate per-location criteria that neglect spatial dependencies, both of which may misclassify brief, spatially coherent episodes or overlook events obscured by these dependencies. This research proposes a dynamically aware, residual-based outlier detection method for the GSTAR model, which operates directly on the space-time residuals. The process involves (i) computing the residuals of the GSTAR model, (ii) identifying outliers based on these residuals, and (iii) incorporating an outlier factor into the model, followed by estimating the parameters of the revised model and reverting to step (i). This technique is iteratively performed until no outliers are identified and the model satisfies the white noise condition. This approach utilizes weekly forest fire hotspot counts from 13 districts in West Kalimantan (June 2023-March 2025), employing a row-standardized Queen Contiguity matrix for spatial weighting. The outcomes of outlier detection utilizing the proposed technique are thereafter compared with those derived from the spatial detection method (Local Moran's I) for each observation period. The findings indicate a more accurate detector, fewer alerts but better calibrated to temporally anomalous events, and a constant decrease in the MSE of GSTAR forecasts one step following the introduction of the indicator. This approach produces a localized and interpretable spatial-temporal signal with minimal computational expense. It is compatible with conventional spatial weight building, offering a viable and reproducible framework for detecting spatial-temporal anomalies in environmental monitoring.