A MGSTAR: An Extension of the Generalized Space-Time Autoregressive Model

Up to now, Generalized Space-Time Autoregressive (GSTAR) models are focused only for univariate spatial-temporal data. This research proposes an extension of GSTAR for multivariate spatial-temporal data, known as Multivariate GSTAR or MGSTAR. Three studies were conducted in this research, i.e., theoretical, simulation, and applied studies. These studies were initially developed based on bivariate spatial-temporal data. A theoretical study was done by developing MGSTAR based on the framework of Vector Autoregressive (VAR) models. In this proposed MGSTAR model, the parameter estimation was obtained by implementing Ordinary Least Square (OLS) method. The simulation study showed that OLS method yielded unbiased estimator. Furthermore, the MGSTAR models have applied for forecasting CO and PM10 at three stations in Surabaya City. The results showed that MGSTAR model could explain well the dynamic relationship between variables and locations. However, based on Root Mean Square Error Prediction (RMSEP), the results showed that MGSTAR model yielded less accurate forecast than ARIMA model due to MGSTAR employed simpler order of Autoregressive. Further research is needed to expand the MGSTAR model with a higher order of Autoregressive, particularly to handle trend and seasonal order.