GLS estimation in python to forecast gross regional domestic product using generalized space–time autoregressive seemingly unrelated regression model

Economic growth is essential for regional economic performance, with gross regional domestic product (GRDP) being a key indicator of economic development over time. In this research case, the GRDP data of various provinces on Java Island from 2010 to 2023 will be used as the variable being studied. The data obtained from the GRDP variable contain spatial and temporal information, requiring an appropriate model to forecast spatiotemporal data, namely, the Generalized Space–Time Autoregressive (GSTAR) model. However, in estimating the parameters, the GSTAR model is unable to detect correlated residuals between equations, resulting in inefficient estimators. Therefore, an appropriate estimation method is needed to address correlated residuals within the seemingly unrelated regression (SUR) framework, namely, the Generalized Least Square (GLS) estimation method. The GSTAR-SUR method is applied to forecast the economic growth rate of Java Island. The optimal model, GSTAR-SUR (11)-I(1) with inverse distance location weights, demonstrates high accuracy with a mean absolute percentage error (MAPE) of 8.451%. Forecasts for Banten, DKI Jakarta, West Java, Central Java, East Java, and DI Yogyakarta predict consistent monthly GRDP increases through December 2024.