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

Abstract

This study aims to develop a model and forecast product sales in four central provinces on the island of Java using the Generalized Space-Time Autoregressive (GSTAR) method. The data used are monthly sales data from DKI Jakarta, West Java, Central Java, and East Java, covering 12 observation periods. The research stages include testing data stationarity using the Augmented Dickey-Fuller (ADF) test, determining the best model based on the Akaike Information Criterion (AIC) criteria, creating a spatial weight matrix using the inverse distance weighting approach, calculating model parameters using the Ordinary Least Squares (OLS) method, and evaluating model performance using Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE). The results show that the best GSTAR(1,1) model was obtained in the Central Java configuration, with an AIC value of 347.892. This model successfully demonstrated a strong spatial relationship with a real spillover effect, particularly the influence of DKI Jakarta on West Java, which reached 72%. The model accuracy level shows an overall MAPE of 48.84% and a total RMSE of 42.749128, with the best performance in Central Java (MAPE: 38.92%) and East Java (MAPE: 45.23%)/. This study shows that a forecasting model that considers both geographical and time factors simultaneously can be effective