SOME COMMENTS ON THE THEOREM PROVIDING STATIONARITY CONDITION FOR GSTAR MODELS IN THE PAPER BY BOROVKOVA et al. Suhartono and Subanar

Generalized Space-Time Autoregressive (GSTAR) model is one of the models that usually used for modeling and forecasting space and time series data. The aim of this paper is to study further about the stationarity conditions for parameters in the GSTAR model and the relation to Vector Autoregressive (VAR) model. We focus on the theoretical study about stationarity condition in GSTAR(11) and the relation to the stationarity condition of parameters in VAR(1). Then, we do an empirical study to give counter examples for the theorem of stationarity condition proposed by Borovkova et al. The results show that the theorem of stationarity condition of parameters in GSTAR(11) model given by Borovkova et al. is incorrect. Additionally, the empirical results also show that GSTAR(11) model could always be represented in VAR(1) model by applying matrix operation to the space and time parameters. Hence, we can also conclude that VAR model, particularly VAR(1), is an extension of GSTAR(11) model with any possibility values of space and time parameters.