Application of Spatial Weight Matrix based on Semivariogram in Space-Time Autoregressive Integrative (STARI) Model for Financial System Forecasting in the Greater Bandung Region

Abstract

The global financial crisis of 2022 had a significant impact on the stability of Indonesia’s financial sector, marked by fiscal expansion and an increase in the money supply. The uneven distribution of liquidity across regions generated disparities in regional inflation, resulting in macroeconomic dynamics that exhibited a complex spatio-temporal structure. These conditions require a forecasting approach capable of capturing spatial and temporal interactions simultaneously. This study applies the Space Time Autoregressive Integrated (STARI) model to describe monthly inflation dynamics that are non-stationary due to inter-regional trends within Bandung Raya area. Spatial dependence is represented through spatial weight matrices constructed using three approaches matrices: uniform weights, inverse-distance weights, and isotropic semivariogram weights derived from population density data. Their effects on forecasting accuracy are compared using the Mean Squared Error (MSE). The novelty of the proposed approach lies in the use of an isotropic semivariogram as the basis for constructing spatial weights, allowing the model to capture continuous and heterogeneous spatial autocorrelation beyond traditional distance-based methods. Model parameters are estimated using Ordinary Least Squares (OLS) method implemented through Python scripts, and model evaluation is conducted using forecasting accuracy criteria and error diagnostics. The results indicate that the STARI(1,1,1) model incorporating semivariogram-based spatial weights outperforms both uniform and inverse-distance weights in terms of forecasting accuracy, because it has a minimum MSE. These findings provide valuable insights for economic policy formulation in Bandung Raya area.