Generalized Space Time Autoregressive Integrated Moving Average with Exogenous (GSTARIMA-X) Models

Abstract

Space time data is data that relates to events at previous times and locations. One of the models that used to analyze space time data is the Generalized Space Time Autoregressive Moving Average (GSTARMA) model. GSTARMA model uses parameters p and λk to represent the time order and spatial order respectively. Hence, this model can be called GSTARMA(p, λk ). Because in fact there are more models with different parameters for different locations, GSTARMA(p, λk ) model is more realistic. If space time data is not stationary, a different order is added so that the model becomes GSTARIMA(p, d, λk ). In modelling sometimes the accuracy of the model can increase by other influence variables. These variables are named exogenous variables. The GSTARIMA model with exogenous variables is named the GSTARIMA-X(p, d, λk ) model. This research aims to examine the model and its estimation of parameters. Model parameters are estimated using the Generalized Least Square (GLS) method. The method in this writing is literature study obtained from several articles, journals, and books that support in achieving research. The results of the study show that with the GLS method, parameter estimates can be obtained with the assumption of time order 1 and spatial order 1.