GSTARX-GLS Model for Spatio-Temporal Data Forecasting

Up to now, there have not been found a research about Generalized Space Time Autoregressive (GSTAR) that involve predictor. In fact, forecasting model in many cases involved predictor(s) both in univariate and multivariate cases such as ARIMAX and VARIMAX models. Moreover, most research about GSTAR models used Ordinary Least Squares (OLS) methods to estimate the parameters model. In many cases, the residuals of GSTAR model have correlation between locations and imply OLS method yields inefficient estimators. Otherwise, Generalized Least Squares (GLS) method that usually be used in Seemingly Unrelated Regression (SUR) model is an appropriate method for estimating parameters of multivariate models when the residuals between equations are correlated. The aim of this study is to propose GSTARX model with GLS method for estimating the parameters, known as GSTARX-GLS model. This research focuses on non metric predictor known as intervention variable. Theoretical study was carried out to develop new model building procedure for GSTARX-GLS model and the results were validated by simulation study. Then, the proposed model was applied for inflation forecasting at several cities in Indonesia. The results showed that GSTARX-GLS model yielded more efficient estimators than the GSTARX-OLS model. It was proved by the smaller standard error of GSTARX-GLS estimator. Additionally, GSTARX-GLS and GSTARX-OLS models gave more accurate inflation prediction in four cities in Indonesia than VARIMAX model.