Spatial-Temporal Modeling of Regional Sales Using Generalized Space Time Autoregressive (GSTAR): Spillover Effect Analysis

This study forecasts healthcare product sales across the provinces of Java Island using the Generalized Space-Time Autoregressive (GSTAR) model. The dataset comprises 48 monthly observations from January 2020 to December 2023 for DKI Jakarta, West Java, Central Java, and East Java. The methodological steps include stationarity testing using the Augmented Dickey–Fuller (ADF) test, model identification based on the Akaike Information Criterion (AIC), spatial weight matrix construction using inverse distance weighting, parameter es timation through Ordinary Least Squares (OLS), and performance evaluation using Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE). The GSTAR(1,1) model is identified as the optimal specification with an AIC value of 1769.47, successfully capturing strong spatial dependencies, including a substantial spillover effect from West Java to DKI Jakarta (0.76). The model exhibits excellent predictive accuracy, with MAPE values of 1.92% (DKI Jakarta), 3.30% (West Java), 7.97% (Central Java), and 4.93% (East Java), resulting in an overall average of 4.53%, classified as highly accurate. The Ljung–Box test further confirms model adequacy, with all residuals meeting independence criteria. Overall, the findings demonstrate that incorporating both spatial and temporal dependencies through GSTAR provides an effective framework for regional sales forecasting and strategic planning across Java Island.