The Space-Time Autoregressive Modelling with Time Correlated Errors for The Number of Vehicles in Purbaleunyi Toll Gates

Abstract

The space-time modelling considers the observations dependence based on time and spatial simultaneously. One of popular models used is the Generalized Space-Time Autoregressive (GSTAR). Most of the GSTAR class models assumed that the errors are uncorrelated and normal distributed. In fact, the dependence of errors is exist. In this paper, the GSTAR model is assumed to have the time correlated errors. The convergence of the parameter estimators is evaluated and the weak consistency is obtained. The illustration is performed by using the number of vehicles passed through Purbaleunyi toll gates. For this data, the GSTAR models be applied and compared between the uncorrelated and time correlated errors assumption of modeling. It is obtained that the GSTAR(1;1) model with time correlated errors, is more appropriate model to predict the number of vehicles passed through the Purbaleunyi toll gates. This appropriate model is well performed when the minimum number of time observations is more than sixty observations.